1.
Particle physics
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Particle physics is the branch of physics that studies the nature of the particles that constitute matter and radiation. By our current understanding, these particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model, in more technical terms, they are described by quantum state vectors in a Hilbert space, which is also treated in quantum field theory. All particles and their interactions observed to date can be described almost entirely by a field theory called the Standard Model. The Standard Model, as formulated, has 61 elementary particles. Those elementary particles can combine to form composite particles, accounting for the hundreds of species of particles that have been discovered since the 1960s. The Standard Model has been found to agree with almost all the tests conducted to date. However, most particle physicists believe that it is a description of nature. In recent years, measurements of mass have provided the first experimental deviations from the Standard Model. The idea that all matter is composed of elementary particles dates from at least the 6th century BC, in the 19th century, John Dalton, through his work on stoichiometry, concluded that each element of nature was composed of a single, unique type of particle. Throughout the 1950s and 1960s, a variety of particles were found in collisions of particles from increasingly high-energy beams. It was referred to informally as the particle zoo, the current state of the classification of all elementary particles is explained by the Standard Model. It describes the strong, weak, and electromagnetic fundamental interactions, the species of gauge bosons are the gluons, W−, W+ and Z bosons, and the photons. The Standard Model also contains 24 fundamental particles, which are the constituents of all matter, finally, the Standard Model also predicted the existence of a type of boson known as the Higgs boson. Early in the morning on 4 July 2012, physicists with the Large Hadron Collider at CERN announced they had found a new particle that behaves similarly to what is expected from the Higgs boson, the worlds major particle physics laboratories are, Brookhaven National Laboratory. Its main facility is the Relativistic Heavy Ion Collider, which collides heavy ions such as gold ions and it is the worlds first heavy ion collider, and the worlds only polarized proton collider. Its main projects are now the electron-positron colliders VEPP-2000, operated since 2006 and its main project is now the Large Hadron Collider, which had its first beam circulation on 10 September 2008, and is now the worlds most energetic collider of protons. It also became the most energetic collider of heavy ions after it began colliding lead ions and its main facility is the Hadron Elektron Ring Anlage, which collides electrons and positrons with protons
2.
Isospin
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In nuclear physics and particle physics, isospin is a quantum number related to the strong interaction. For example, a pair can be coupled in a state of total isospin 1 or 0. It is a quantity and the name derives from the fact that the mathematical structures used to describe it are very similar to those used to describe the intrinsic angular momentum. This term was derived from isotopic spin, a term to which nuclear physicists prefer isobaric spin. Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons, Isospin symmetry remains an important concept in particle physics. A close examination of this symmetry, historically, led directly to the discovery and understanding of quarks, although the proton has a positive electric charge, and the neutron is neutral, they are almost identical in all other aspects. The strength of the interaction between any pair of nucleons is the same, independent of whether they are interacting as protons or as neutrons. This behavior is not unlike the electron, where there are two states based on their spin. A change in spin turns an electron into a positron and vice versa, other properties of the particle are conserved in this case. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron, in 1937, Eugene Wigner introduced the term isospin to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated. Thus, isospin was introduced as a well before the development of the quark model, in the 1960s. Similar to a spin 1⁄2 particle, which has two states, protons and neutrons were said to be of isospin 1⁄2, the proton and neutron were then associated with different isospin projections I3 = + 1⁄2 and − 1⁄2 respectively. Protons and neutrons were then grouped together as nucleons because they both have nearly the same mass and interact in nearly the way, if the electromagnetic interaction is neglected. It was convenient to them as being different states of the same particle. When constructing a theory of nuclear forces, one could simply assume that it does not depend on isospin. These considerations would also prove useful in the analysis of meson-nucleon interactions after the discovery of the pions in 1947, the three pions could be assigned to an isospin triplet with I =1 and I3 = +1,0 or −1. By assuming that isospin was conserved by nuclear interactions, the new mesons were more easily accommodated by nuclear theory and this multiplet structure was combined with strangeness in Murray Gell-Manns eightfold way, ultimately leading to the quark model and quantum chromodynamics. Observations of the light baryons imply that some of these particles are so similar in terms of their interactions that they can be treated as different states of the same particle
3.
Electric charge
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Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of charges, positive and negative. Like charges repel and unlike attract, an absence of net charge is referred to as neutral. An object is charged if it has an excess of electrons. The SI derived unit of charge is the coulomb. In electrical engineering, it is common to use the ampere-hour. The symbol Q often denotes charge, early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that dont require consideration of quantum effects. The electric charge is a conserved property of some subatomic particles. Electrically charged matter is influenced by, and produces, electromagnetic fields, the interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces. 602×10−19 coulombs. The proton has a charge of +e, and the electron has a charge of −e, the study of charged particles, and how their interactions are mediated by photons, is called quantum electrodynamics. Charge is the property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter. Electric charge is a property of many subatomic particles. The charges of free-standing particles are integer multiples of the charge e. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge, robert Millikans oil drop experiment demonstrated this fact directly, and measured the elementary charge. By convention, the charge of an electron is −1, while that of a proton is +1, charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. The charge of an antiparticle equals that of the corresponding particle, quarks have fractional charges of either −1/3 or +2/3, but free-standing quarks have never been observed. The electric charge of an object is the sum of the electric charges of the particles that make it up. An ion is an atom that has lost one or more electrons, giving it a net charge, or that has gained one or more electrons
4.
Hypercharge
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The concept of hypercharge combines and unifies isospin and flavour into a single charge operator. Hypercharge in particle physics is a number relating the strong interactions of the SU model. Isospin is defined in the SU model while the SU model defines hypercharge, SU weight diagrams are 2-dimensional with the coordinates referring to two quantum numbers, Iz, which is the z-component of isospin and Y, which is the hypercharge. Mathematically, hypercharge is Y = S + C + B ′ + T + B, strong interactions conserve hypercharge, but weak interactions do not. The Gell-Mann–Nishijima formula relates isospin and electric charge Q = I3 +12 Y, isospin creates multiplets of particles whose average charge is related to the hypercharge by, Y =2 Q ¯. Since the hypercharge is the same for all members of a multiplet, the SU model has multiplets characterized by a quantum number J, which is the total angular momentum. Each multiplet consists of 2J +1 substates with equally spaced values of Jz, forming a symmetric arrangement seen in atomic spectra and isospin. This formalizes the observation that certain strong baryon decays were not observed, leading to the prediction of the mass, strangeness, the SU has supermultiplets containing SU multiplets. SU now needs 2 numbers to all its sub-states which are denoted by λ1. Specifies the number of points in the topmost side of the hexagon while specifies the number of points on the bottom side, the nucleon group have an average charge of +1/2, so they both have hypercharge Y =1. From the Gell-Mann–Nishijima formula we know that proton has isospin I3 = +1/2 and this also works for quarks, for the up quark, with a charge of +2/3, and an I3 of +1/2, we deduce a hypercharge of 1/3, due to its baryon number. For a strange quark, with charge −1/3, a number of 1/3 and strangeness of −1 we get a hypercharge Y = −2/3. That means that a strange quark makes a singlet of its own, while up, hypercharge was a concept developed in the 1960s, to organize groups of particles in the particle zoo and to develop ad hoc conservation laws based on their observed transformations. With the advent of the model, it is now obvious that, hypercharge Y is the following combination of the numbers of up, down, strange quarks, charm quarks, top quarks and bottom quarks. Weak hypercharge, however, remains of use in various theories of the electroweak interaction. Introduction to atomic and nuclear physics
5.
Elementary particle
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In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus, it is unknown whether it is composed of other particles. A particle containing two or more elementary particles is a composite particle, soon, subatomic constituents of the atom were identified. As the 1930s opened, the electron and the proton had been observed, along with the photon, via quantum theory, protons and neutrons were found to contain quarks—up quarks and down quarks—now considered elementary particles. And within a molecule, the three degrees of freedom can separate via wavefunction into three quasiparticles. Yet a free electron—which, not orbiting a nucleus, lacks orbital motion—appears unsplittable. Meanwhile, an elementary boson mediating gravitation—the graviton—remains hypothetical, all elementary particles are—depending on their spin—either bosons or fermions. These are differentiated via the theorem of quantum statistics. Particles of half-integer spin exhibit Fermi–Dirac statistics and are fermions, Particles of integer spin, in other words full-integer, exhibit Bose–Einstein statistics and are bosons. In the Standard Model, elementary particles are represented for predictive utility as point particles, though extremely successful, the Standard Model is limited to the microcosm by its omission of gravitation and has some parameters arbitrarily added but unexplained. According to the current models of big bang nucleosynthesis, the composition of visible matter of the universe should be about 75% hydrogen. Neutrons are made up of one up and two down quark, while protons are made of two up and one down quark. Since the other elementary particles are so light or so rare when compared to atomic nuclei. Therefore, one can conclude that most of the mass of the universe consists of protons and neutrons. Some estimates imply that there are roughly 1080 baryons in the observable universe, the number of protons in the observable universe is called the Eddington number. Other estimates imply that roughly 1097 elementary particles exist in the universe, mostly photons, gravitons. However, the Standard Model is widely considered to be a theory rather than a truly fundamental one. The 12 fundamental fermionic flavours are divided into three generations of four particles each, six of the particles are quarks. The remaining six are leptons, three of which are neutrinos, and the three of which have an electric charge of −1, the electron and its two cousins, the muon and the tau
6.
Standard Model
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The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong interactions, as well as classifying all the elementary particles known. It was developed throughout the half of the 20th century. The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks, since then, discoveries of the top quark, the tau neutrino, and the Higgs boson have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results and it does not incorporate the full theory of gravitation as described by general relativity, or account for the accelerating expansion of the Universe. The model does not contain any viable dark matter particle that all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations, the development of the Standard Model was driven by theoretical and experimental particle physicists alike. For theorists, the Standard Model is a paradigm of a field theory. The first step towards the Standard Model was Sheldon Glashows discovery in 1961 of a way to combine the electromagnetic, in 1967 Steven Weinberg and Abdus Salam incorporated the Higgs mechanism into Glashows electroweak interaction, giving it its modern form. The Higgs mechanism is believed to rise to the masses of all the elementary particles in the Standard Model. This includes the masses of the W and Z bosons, the W± and Z0 bosons were discovered experimentally in 1983, and the ratio of their masses was found to be as the Standard Model predicted. The theory of the interaction, to which many contributed, acquired its modern form around 1973–74. At present, matter and energy are best understood in terms of the kinematics, to date, physics has reduced the laws governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. The Standard Model includes members of classes of elementary particles. All particles can be summarized as follows, The Standard Model includes 12 elementary particles of spin known as fermions. According to the theorem, fermions respect the Pauli exclusion principle. Each fermion has a corresponding antiparticle, the fermions of the Standard Model are classified according to how they interact. There are six quarks, and six leptons, pairs from each classification are grouped together to form a generation, with corresponding particles exhibiting similar physical behavior. The defining property of the quarks is that they carry color charge, a phenomenon called color confinement results in quarks being very strongly bound to one another, forming color-neutral composite particles containing either a quark and an antiquark or three quarks
7.
Quark
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A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, due to a phenomenon known as color confinement, quarks are never directly observed or found in isolation, they can be found only within hadrons, such as baryons and mesons. For this reason, much of what is known about quarks has been drawn from observations of the hadrons themselves, Quarks have various intrinsic properties, including electric charge, mass, color charge, and spin. There are six types of quarks, known as flavors, up, down, strange, charm, top, up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up and down quarks through a process of particle decay, the transformation from a higher mass state to a lower mass state. Because of this, up and down quarks are generally stable and the most common in the universe, whereas strange, charm, bottom, and top quarks can only be produced in high energy collisions. For every quark flavor there is a type of antiparticle, known as an antiquark. The quark model was proposed by physicists Murray Gell-Mann and George Zweig in 1964. Accelerator experiments have provided evidence for all six flavors, the top quark was the last to be discovered at Fermilab in 1995. The Standard Model is the theoretical framework describing all the known elementary particles. This model contains six flavors of quarks, named up, down, strange, charm, bottom, antiparticles of quarks are called antiquarks, and are denoted by a bar over the symbol for the corresponding quark, such as u for an up antiquark. As with antimatter in general, antiquarks have the mass, mean lifetime, and spin as their respective quarks. Quarks are spin- 1⁄2 particles, implying that they are fermions according to the spin-statistics theorem and they are subject to the Pauli exclusion principle, which states that no two identical fermions can simultaneously occupy the same quantum state. This is in contrast to bosons, any number of which can be in the same state, unlike leptons, quarks possess color charge, which causes them to engage in the strong interaction. The resulting attraction between different quarks causes the formation of composite particles known as hadrons, there are two families of hadrons, baryons, with three valence quarks, and mesons, with a valence quark and an antiquark. The most common baryons are the proton and the neutron, the blocks of the atomic nucleus. A great number of hadrons are known, most of them differentiated by their quark content, the existence of exotic hadrons with more valence quarks, such as tetraquarks and pentaquarks, has been conjectured but not proven. However, on 13 July 2015, the LHCb collaboration at CERN reported results consistent with pentaquark states, elementary fermions are grouped into three generations, each comprising two leptons and two quarks
8.
Lepton
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A lepton is an elementary, half-integer spin particle that does not undergo strong interactions. Two main classes of leptons exist, charged leptons, and neutral leptons, the best known of all leptons is the electron. There are six types of leptons, known as flavours, forming three generations, electrons have the least mass of all the charged leptons. The heavier muons and taus will rapidly change into electrons and neutrinos through a process of particle decay, thus electrons are stable and the most common charged lepton in the universe, whereas muons and taus can only be produced in high energy collisions. Leptons have various properties, including electric charge, spin. Unlike quarks however, leptons are not subject to the strong interaction, for every lepton flavor there is a corresponding type of antiparticle, known as an antilepton, that differs from the lepton only in that some of its properties have equal magnitude but opposite sign. However, according to theories, neutrinos may be their own antiparticle. The first charged lepton, the electron, was theorized in the century by several scientists and was discovered in 1897 by J. J. Thomson. The next lepton to be observed was the muon, discovered by Carl D. Anderson in 1936, after investigation, it was realized that the muon did not have the expected properties of a meson, but rather behaved like an electron, only with higher mass. It took until 1947 for the concept of leptons as a family of particle to be proposed, the first neutrino, the electron neutrino, was proposed by Wolfgang Pauli in 1930 to explain certain characteristics of beta decay. It was first observed in the Cowan–Reines neutrino experiment conducted by Clyde Cowan, the muon neutrino was discovered in 1962 by Leon M. The tau neutrino remained elusive until July 2000, when the DONUT collaboration from Fermilab announced its discovery, Leptons are an important part of the Standard Model. Electrons are one of the components of atoms, alongside protons and neutrons, exotic atoms with muons and taus instead of electrons can also be synthesized, as well as lepton–antilepton particles such as positronium. The name lepton comes from the Greek λεπτός leptós, fine, small, thin, Lepton was first used by physicist Léon Rosenfeld in 1948, Following a suggestion of Prof. C. Møller, I adopt—as a pendant to nucleon—the denomination lepton to denote a particle of small mass, the etymology incorrectly implies that all the leptons are of small mass. However, the mass of the tau is nearly twice that of the proton, the first lepton identified was the electron, discovered by J. J. Thomson and his team of British physicists in 1897, then in 1930 Wolfgang Pauli postulated the electron neutrino to preserve conservation of energy, conservation of momentum, and conservation of angular momentum in beta decay. Pauli theorized that a particle was carrying away the difference between the energy, momentum, and angular momentum of the initial and observed final particles
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Subatomic particle
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In the physical sciences, subatomic particles are particles much smaller than atoms. There are two types of particles, elementary particles, which according to current theories are not made of other particles. Particle physics and nuclear physics study these particles and how they interact, in particle physics, the concept of a particle is one of several concepts inherited from classical physics. But it also reflects the understanding that at the quantum scale matter. The idea of a particle underwent serious rethinking when experiments showed that light could behave like a stream of particles as well as exhibit wave-like properties and this led to the new concept of wave–particle duality to reflect that quantum-scale particles behave like both particles and waves. Another new concept, the uncertainty principle, states that some of their properties taken together, such as their simultaneous position and momentum, in more recent times, wave–particle duality has been shown to apply not only to photons but to increasingly massive particles as well. Interactions of particles in the framework of field theory are understood as creation and annihilation of quanta of corresponding fundamental interactions. This blends particle physics with field theory, any subatomic particle, like any particle in the 3-dimensional space that obeys laws of quantum mechanics, can be either a boson or a fermion. Various extensions of the Standard Model predict the existence of a graviton particle. Composite subatomic particles are bound states of two or more elementary particles, for example, a proton is made of two up quarks and one down quark, while the atomic nucleus of helium-4 is composed of two protons and two neutrons. The neutron is made of two quarks and one up quark. Composite particles include all hadrons, these include baryons and mesons, in special relativity, the energy of a particle at rest equals its mass times the speed of light squared, E = mc2. That is, mass can be expressed in terms of energy, if a particle has a frame of reference where it lies at rest, then it has a positive rest mass and is referred to as massive. Baryons tend to have greater mass than mesons, which in turn tend to be heavier than leptons and it is also certain that any particle with an electric charge is massive. These include the photon and gluon, although the latter cannot be isolated, through the work of Albert Einstein, Satyendra Nath Bose, Louis de Broglie, and many others, current scientific theory holds that all particles also have a wave nature. This has been verified not only for elementary particles but also for compound particles like atoms, interactions between particles have been scrutinized for many centuries, and a few simple laws underpin how particles behave in collisions and interactions. These are the basics of Newtonian mechanics, a series of statements and equations in Philosophiae Naturalis Principia Mathematica. The negatively charged electron has an equal to 1⁄1837 or 1836 of that of a hydrogen atom
10.
Force
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In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity, force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity and it is measured in the SI unit of newtons and represented by the symbol F. The original form of Newtons second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. In an extended body, each part usually applies forces on the adjacent parts, such internal mechanical stresses cause no accelation of that body as the forces balance one another. Pressure, the distribution of small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of materials, or flow in fluids. In part this was due to an understanding of the sometimes non-obvious force of friction. A fundamental error was the belief that a force is required to maintain motion, most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years, the Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known, in order of decreasing strength, they are, strong, electromagnetic, weak, high-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotles view, the sphere contained four elements that come to rest at different natural places therein. Aristotle believed that objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground. He distinguished between the tendency of objects to find their natural place, which led to natural motion, and unnatural or forced motion
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Point particle
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A point particle is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension, being zero-dimensional, a point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context. For example, from far away, an object of any shape will look. In the theory of gravity, physicists discuss a point mass, meaning a point particle with a nonzero mass. Likewise, in electromagnetism, physicists discuss a point charge, a point particle with a nonzero charge, sometimes, due to specific combinations of properties, extended objects behave as point-like even in their immediate vicinity. For example, the orbit of an electron in the hydrogen atom occupies a volume of ~10−30 m3. Elementary particles are called point particles, but this is in a different sense than discussed above. When a point particle has a property, such as mass or charge, concentrated at a single point in space. A common use for point mass lies in the analysis of the gravitational fields, when analyzing the gravitational forces in a system, it becomes impossible to account for every unit of mass individually. However, a spherically symmetric body affects external objects gravitationally as if all of its mass were concentrated at its center, to calculate such a point mass, an integration is carried out over the entire range of the random variable, on the probability density of the continuous part. After equating this integral to 1, the point mass can be found by further calculation, a point charge is an idealized model of a particle which has an electric charge. A point charge is a charge at a mathematical point with no dimensions. The fundamental equation of electrostatics is Coulombs law, which describes the force between two point charges. The electric field associated with a point charge increases to infinity as the distance from the point charge decreases towards zero making energy of point charge infinite. Earnshaws theorem states that a collection of point charges cannot be maintained in an equilibrium configuration solely by the interaction of the charges. In quantum mechanics, there is a distinction between a particle and a composite particle. An elementary particle, such as an electron, quark, or photon, is a particle with no structure, whereas a composite particle. However, neither elementary nor composite particles are spatially localized, because of the Heisenberg uncertainty principle, the particle wavepacket always occupies a nonzero volume
12.
Particle
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A particle is a minute fragment or quantity of matter. In the physical sciences, a particle is a small localized object to which can be ascribed several physical or chemical properties such as volume or mass. Particles can also be used to create models of even larger objects depending on their density. The term particle is rather general in meaning, and is refined as needed by various scientific fields, something that is composed of particles may be referred to as being particulate. However, the particulate is most frequently used to refer to pollutants in the Earths atmosphere. The concept of particles is particularly useful when modelling nature, as the treatment of many phenomena can be complex. It can be used to make simplifying assumptions concerning the processes involved, francis Sears and Mark Zemansky, in University Physics, give the example of calculating the landing location and speed of a baseball thrown in the air. The treatment of large numbers of particles is the realm of statistical physics, the term particle is usually applied differently to three classes of sizes. The term macroscopic particle, usually refers to particles much larger than atoms and these are usually abstracted as point-like particles, or even invisible. This is even though they have volumes, shapes, structures, examples of macroscopic particles would include powder, dust, sand, pieces of debris during a car accident, or even objects as big as the stars of a galaxy. Another type, microscopic particles usually refers to particles of sizes ranging from atoms to molecules, such as carbon dioxide, nanoparticles and these particles are studied in chemistry, as well as atomic and molecular physics. The smallest of particles are the particles, which refer to particles smaller than atoms. These particles are studied in particle physics, because of their extremely small size, the study of microscopic and subatomic particles fall in the realm of quantum mechanics. Particles can also be classified according to composition, composite particles refer to particles that have composition – that is particles which are made of other particles. For example, an atom is made of six protons, eight neutrons. By contrast, elementary particles refer to particles that are not made of other particles, according to our current understanding of the world, only a very small number of these exist, such as the leptons, quarks or gluons. However it is possible some of these might turn up to be composite particles after all. While composite particles can very often be considered point-like, elementary particles are truly punctual, both elementary and composite particles, are known to undergo particle decay
13.
Momentum
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In classical mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object, quantified in kilogram-meters per second. It is dimensionally equivalent to impulse, the product of force and time, Newtons second law of motion states that the change in linear momentum of a body is equal to the net impulse acting on it. If the truck were lighter, or moving slowly, then it would have less momentum. Linear momentum is also a quantity, meaning that if a closed system is not affected by external forces. In classical mechanics, conservation of momentum is implied by Newtons laws. It also holds in special relativity and, with definitions, a linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory. It is ultimately an expression of one of the symmetries of space and time. Linear momentum depends on frame of reference, observers in different frames would find different values of linear momentum of a system. But each would observe that the value of linear momentum does not change with time, momentum has a direction as well as magnitude. Quantities that have both a magnitude and a direction are known as vector quantities, because momentum has a direction, it can be used to predict the resulting direction of objects after they collide, as well as their speeds. Below, the properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations, the momentum of a particle is traditionally represented by the letter p. It is the product of two quantities, the mass and velocity, p = m v, the units of momentum are the product of the units of mass and velocity. In SI units, if the mass is in kilograms and the velocity in meters per second then the momentum is in kilogram meters/second, in cgs units, if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters/second. Being a vector, momentum has magnitude and direction, for example, a 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has a momentum of 1 kg m/s due north measured from the ground. The momentum of a system of particles is the sum of their momenta, if two particles have masses m1 and m2, and velocities v1 and v2, the total momentum is p = p 1 + p 2 = m 1 v 1 + m 2 v 2. If all the particles are moving, the center of mass will generally be moving as well, if the center of mass is moving at velocity vcm, the momentum is, p = m v cm. This is known as Eulers first law, if a force F is applied to a particle for a time interval Δt, the momentum of the particle changes by an amount Δ p = F Δ t
14.
Quantum field theory
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QFT treats particles as excited states of the underlying physical field, so these are called field quanta. In quantum field theory, quantum mechanical interactions among particles are described by interaction terms among the corresponding underlying quantum fields and these interactions are conveniently visualized by Feynman diagrams, which are a formal tool of relativistically covariant perturbation theory, serving to evaluate particle processes. The first achievement of quantum theory, namely quantum electrodynamics, is still the paradigmatic example of a successful quantum field theory. Ordinarily, quantum mechanics cannot give an account of photons which constitute the prime case of relativistic particles, since photons have rest mass zero, and correspondingly travel in the vacuum at the speed c, a non-relativistic theory such as ordinary QM cannot give even an approximate description. Photons are implicit in the emission and absorption processes which have to be postulated, for instance, the formalism of QFT is needed for an explicit description of photons. In fact most topics in the development of quantum theory were related to the interaction of radiation and matter. However, quantum mechanics as formulated by Dirac, Heisenberg, and Schrödinger in 1926–27 started from atomic spectra, as soon as the conceptual framework of quantum mechanics was developed, a small group of theoreticians tried to extend quantum methods to electromagnetic fields. A good example is the paper by Born, Jordan & Heisenberg. The basic idea was that in QFT the electromagnetic field should be represented by matrices in the way that position. The ideas of QM were thus extended to systems having a number of degrees of freedom. The inception of QFT is usually considered to be Diracs famous 1927 paper on The quantum theory of the emission and absorption of radiation, here Dirac coined the name quantum electrodynamics for the part of QFT that was developed first. Employing the theory of the harmonic oscillator, Dirac gave a theoretical description of how photons appear in the quantization of the electromagnetic radiation field. Later, Diracs procedure became a model for the quantization of fields as well. These first approaches to QFT were further developed during the three years. P. Jordan introduced creation and annihilation operators for fields obeying Fermi–Dirac statistics and these differ from the corresponding operators for Bose–Einstein statistics in that the former satisfy anti-commutation relations while the latter satisfy commutation relations. The methods of QFT could be applied to derive equations resulting from the treatment of particles, e. g. the Dirac equation, the Klein–Gordon equation. Schweber points out that the idea and procedure of second quantization goes back to Jordan, in a number of papers from 1927, some difficult problems concerning commutation relations, statistics, and Lorentz invariance were eventually solved. The first comprehensive account of a theory of quantum fields, in particular
15.
Weak interaction
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In particle physics, the weak interaction is one of the four known fundamental interactions of nature, alongside the strong interaction, electromagnetism, and gravitation. The weak interaction is responsible for radioactive decay, which plays an role in nuclear fission. The theory of the interaction is sometimes called quantum flavourdynamics, in analogy with the terms QCD dealing with the strong interaction. However the term QFD is rarely used because the force is best understood in terms of electro-weak theory. The Standard Model of particle physics, which does not address gravity, provides a framework for understanding how the electromagnetic, weak. An interaction occurs when two particles, typically but not necessarily half-integer spin fermions, exchange integer-spin, force-carrying bosons, the fermions involved in such exchanges can be either elementary or composite, although at the deepest levels, all weak interactions ultimately are between elementary particles. In the case of the interaction, fermions can exchange three distinct types of force carriers known as the W+, W−, and Z bosons. The mass of each of these bosons is far greater than the mass of a proton or neutron, the force is in fact termed weak because its field strength over a given distance is typically several orders of magnitude less than that of the strong nuclear force or electromagnetic force. During the quark epoch of the universe, the electroweak force separated into the electromagnetic. Important examples of the weak interaction include beta decay, and the fusion of hydrogen into deuterium that powers the Suns thermonuclear process, most fermions will decay by a weak interaction over time. Such decay makes radiocarbon dating possible, as carbon-14 decays through the interaction to nitrogen-14. It can also create radioluminescence, commonly used in tritium illumination, quarks, which make up composite particles like neutrons and protons, come in six flavours – up, down, strange, charm, top and bottom – which give those composite particles their properties. The weak interaction is unique in that it allows for quarks to swap their flavour for another, the swapping of those properties is mediated by the force carrier bosons. Also, the interaction is the only fundamental interaction that breaks parity-symmetry, and similarly. In 1933, Enrico Fermi proposed the first theory of the weak interaction and he suggested that beta decay could be explained by a four-fermion interaction, involving a contact force with no range. However, it is described as a non-contact force field having a finite range. The existence of the W and Z bosons was not directly confirmed until 1983, the weak interaction is unique in a number of respects, It is the only interaction capable of changing the flavour of quarks. It is the interaction that violates P or parity-symmetry
16.
Invariant mass
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More precisely, it is a characteristic of the systems total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center of momentum frame exists for the system, then the invariant mass of a system is equal to its mass in that rest frame. In other reference frames, where the momentum is nonzero, the total mass of the system is greater than the invariant mass. Due to mass-energy equivalence, the rest energy of the system is simply the invariant mass times the speed of light squared, similarly, the total energy of the system is its total mass times the speed of light squared. Systems whose four-momentum is a null vector have zero invariant mass, a physical object or particle moving faster than the speed of light would have space-like four-momenta, and these do not appear to exist. Any time-like four-momentum possesses a frame where the momentum is zero. In this case, invariant mass is positive and is referred to as the rest mass, if objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects rest masses. This is also equal to the energy of the system divided by c2. See mass–energy equivalence for a discussion of definitions of mass, for example, a scale would measure the kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass. The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, for an isolated massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity. Thus, an observer can always be placed to move along with it. In this frame, which is the center of momentum frame, the momentum is zero. In this frame, which exists under these assumptions, the invariant mass of the system is equal to the system energy divided by c2. This total energy in the center of momentum frame, is the energy which the system may be observed to have. Note that for reasons above, such a rest frame does not exist for single photons, when two or more photons move in different directions, however, a center of mass frame exists. Thus, the mass of a system of several photons moving in different directions is positive, for example, rest mass and invariant mass are zero for individual photons even though they may add mass to the invariant mass of systems. For this reason, invariant mass is in not an additive quantity. Consider the simple case of system, where object A is moving towards another object B which is initially at rest
17.
Quantum state
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In quantum physics, quantum state refers to the state of an isolated quantum system. A quantum state provides a probability distribution for the value of each observable, knowledge of the quantum state together with the rules for the systems evolution in time exhausts all that can be predicted about the systems behavior. A mixture of states is again a quantum state. Quantum states that cannot be written as a mixture of states are called pure quantum states. Mathematically, a quantum state can be represented by a ray in a Hilbert space over the complex numbers. The ray is a set of nonzero vectors differing by just a scalar factor, any of them can be chosen as a state vector to represent the ray. A unit vector is usually picked, but its phase factor can be chosen freely anyway, nevertheless, such factors are important when state vectors are added together to form a superposition. Hilbert space is a generalization of the ordinary Euclidean space and it all possible pure quantum states of the given system. If this Hilbert space, by choice of representation, is exhibited as a function space, a more complicated case is given by the spin part of a state vector | ψ ⟩ =12, which involves superposition of joint spin states for two particles with spin 1⁄2. A mixed quantum state corresponds to a mixture of pure states, however. Mixed states are described by so-called density matrices, a pure state can also be recast as a density matrix, in this way, pure states can be represented as a subset of the more general mixed states. For example, if the spin of an electron is measured in any direction, e. g. with a Stern–Gerlach experiment, the Hilbert space for the electrons spin is therefore two-dimensional. A mixed state, in case, is a 2 ×2 matrix that is Hermitian, positive-definite. These probability distributions arise for both mixed states and pure states, it is impossible in quantum mechanics to prepare a state in all properties of the system are fixed. This is exemplified by the uncertainty principle, and reflects a difference between classical and quantum physics. Even in quantum theory, however, for every observable there are states that have an exact. In the mathematical formulation of mechanics, pure quantum states correspond to vectors in a Hilbert space. The operator serves as a function which acts on the states of the system
18.
Quantum superposition
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Quantum superposition is a fundamental principle of quantum mechanics. Mathematically, it refers to a property of solutions to the Schrödinger equation, since the Schrödinger equation is linear, an example of a physically observable manifestation of superposition is interference peaks from an electron wave in a double-slit experiment. Another example is a logical qubit state, as used in quantum information processing. Here |0 ⟩ is the Dirac notation for the state that will always give the result 0 when converted to classical logic by a measurement. Likewise |1 ⟩ is the state that will convert to 1. The numbers that describe the amplitudes for different possibilities define the kinematics, the dynamics describes how these numbers change with time. This list is called the vector, and formally it is an element of a Hilbert space. The quantities that describe how they change in time are the transition probabilities K x → y, which gives the probability that, starting at x, the particle ends up at y time t later. When no time passes, nothing changes, for 0 elapsed time K x → y = δ x y, the K matrix is zero except from a state to itself. So in the case that the time is short, it is better to talk about the rate of change of the probability instead of the change in the probability. Quantum amplitudes give the rate at which amplitudes change in time, the reason it is multiplied by i is that the condition that U is unitary translates to the condition, = I H † − H =0 which says that H is Hermitian. The eigenvalues of the Hermitian matrix H are real quantities, which have an interpretation as energy levels. For a particle that has equal amplitude to move left and right, the Hermitian matrix H is zero except for nearest neighbors, where it has the value c. If the coefficient is constant, the condition that H is Hermitian demands that the amplitude to move to the left is the complex conjugate of the amplitude to move to the right. By redefining the phase of the wavefunction in time, ψ → ψ e i 2 c t, but this phase rotation introduces a linear term. I d ψ n d t = c ψ n +1 −2 c ψ n + c ψ n −1, the analogy between quantum mechanics and probability is very strong, so that there are many mathematical links between them. The analogous expression in quantum mechanics is the path integral, a generic transition matrix in probability has a stationary distribution, which is the eventual probability to be found at any point no matter what the starting point. If there is a probability for any two paths to reach the same point at the same time, this stationary distribution does not depend on the initial conditions
19.
Atomic physics
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Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and this comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions. The term atomic physics can be associated with power and nuclear weapons, due to the synonymous use of atomic. Physicists distinguish between atomic physics — which deals with the atom as a system consisting of a nucleus and electrons — and nuclear physics, which considers atomic nuclei alone. As with many fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of atomic, molecular. Physics research groups are usually so classified, Atomic physics primarily considers atoms in isolation. Atomic models will consist of a nucleus that may be surrounded by one or more bound electrons. It is not concerned with the formation of molecules, nor does it examine atoms in a state as condensed matter. It is concerned with such as ionization and excitation by photons or collisions with atomic particles. This means that the atoms can be treated as if each were in isolation. By this consideration atomic physics provides the underlying theory in physics and atmospheric physics. Electrons form notional shells around the nucleus and these are normally in a ground state but can be excited by the absorption of energy from light, magnetic fields, or interaction with a colliding particle. Electrons that populate a shell are said to be in a bound state, the energy necessary to remove an electron from its shell is called the binding energy. Any quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy, the atom is said to have undergone the process of ionization. If the electron absorbs a quantity of less than the binding energy. After a certain time, the electron in a state will jump to a lower state. In a neutral atom, the system will emit a photon of the difference in energy, if an inner electron has absorbed more than the binding energy, then a more outer electron may undergo a transition to fill the inner orbital. The Auger effect allows one to multiply ionize an atom with a single photon, there are rather strict selection rules as to the electronic configurations that can be reached by excitation by light — however there are no such rules for excitation by collision processes
20.
Electron
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The electron is a subatomic particle, symbol e− or β−, with a negative elementary electric charge. Electrons belong to the first generation of the lepton particle family, the electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the include a intrinsic angular momentum of a half-integer value, expressed in units of the reduced Planck constant. As it is a fermion, no two electrons can occupy the same state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of particles and waves, they can collide with other particles and can be diffracted like light. Since an electron has charge, it has an electric field. Electromagnetic fields produced from other sources will affect the motion of an electron according to the Lorentz force law, electrons radiate or absorb energy in the form of photons when they are accelerated. Laboratory instruments are capable of trapping individual electrons as well as electron plasma by the use of electromagnetic fields, special telescopes can detect electron plasma in outer space. Electrons are involved in applications such as electronics, welding, cathode ray tubes, electron microscopes, radiation therapy, lasers, gaseous ionization detectors. Interactions involving electrons with other particles are of interest in fields such as chemistry. The Coulomb force interaction between the positive protons within atomic nuclei and the negative electrons without, allows the composition of the two known as atoms, ionization or differences in the proportions of negative electrons versus positive nuclei changes the binding energy of an atomic system. The exchange or sharing of the electrons between two or more atoms is the cause of chemical bonding. In 1838, British natural philosopher Richard Laming first hypothesized the concept of a quantity of electric charge to explain the chemical properties of atoms. Irish physicist George Johnstone Stoney named this charge electron in 1891, electrons can also participate in nuclear reactions, such as nucleosynthesis in stars, where they are known as beta particles. Electrons can be created through beta decay of isotopes and in high-energy collisions. The antiparticle of the electron is called the positron, it is identical to the electron except that it carries electrical, when an electron collides with a positron, both particles can be totally annihilated, producing gamma ray photons. The ancient Greeks noticed that amber attracted small objects when rubbed with fur, along with lightning, this phenomenon is one of humanitys earliest recorded experiences with electricity. In his 1600 treatise De Magnete, the English scientist William Gilbert coined the New Latin term electricus, both electric and electricity are derived from the Latin ēlectrum, which came from the Greek word for amber, ἤλεκτρον
21.
Electron shell
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In chemistry and atomic physics, an electron shell, or a principal energy level, may be thought of as an orbit followed by electrons around an atoms nucleus. The closest shell to the nucleus is called the 1 shell, followed by the 2 shell, then the 3 shell, the shells correspond with the principal quantum numbers or are labeled alphabetically with letters used in the X-ray notation. Each shell can contain only a number of electrons, The first shell can hold up to two electrons, the second shell can hold up to eight electrons, the third shell can hold up to 18. The general formula is that the nth shell can in principle hold up to 2 electrons, since electrons are electrically attracted to the nucleus, an atoms electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a requirement, atoms may have two or even three incomplete outer shells. For an explanation of why electrons exist in these shells see electron configuration, the electrons in the outermost occupied shell determine the chemical properties of the atom, it is called the valence shell. Each shell consists of one or more subshells, and each consists of one or more atomic orbitals. The shell terminology comes from Arnold Sommerfelds modification of the Bohr model, sommerfeld retained Bohrs planetary model, but added mildly elliptical orbits to explain the fine spectroscopic structure of some elements. The multiple electrons with the principal quantum number had close orbits that formed a shell of positive thickness instead of the infinitely thin circular orbit of Bohrs model. The existence of electron shells was first observed experimentally in Charles Barklas, barkla labeled them with the letters K, L, M, N, O, P, and Q. The origin of this terminology was alphabetic, a J series was also suspected, though later experiments indicated that the K absorption lines are produced by the innermost electrons. These letters were found to correspond to the n values 1,2,3. They are used in the spectroscopic Siegbahn notation, the physical chemist Gilbert Lewis was responsible for much of the early development of the theory of the participation of valence shell electrons in chemical bonding. Linus Pauling later generalized and extended the theory while applying insights from quantum mechanics. The electron shells are labeled K, L, M, N, O, P, and Q, or 1,2,3,4,5,6, and 7, going from innermost shell outwards. Electrons in outer shells have higher energy and travel farther from the nucleus than those in inner shells. This makes them important in determining how the atom reacts chemically and behaves as a conductor, because the pull of the atoms nucleus upon them is weaker. In this way, a given elements reactivity is highly dependent upon its electronic configuration, each shell is composed of one or more subshells, which are themselves composed of atomic orbitals
22.
Energy level
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A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy and these discrete values are called energy levels. The energy spectrum of a system with discrete energy levels is said to be quantized. In chemistry and atomic physics, a shell, or a principal energy level. The closest shell to the nucleus is called the 1 shell, followed by the 2 shell, then the 3 shell, the shells correspond with the principal quantum numbers or are labeled alphabetically with letters used in the X-ray notation. Each shell can contain only a number of electrons, The first shell can hold up to two electrons, the second shell can hold up to eight electrons, the third shell can hold up to 18. The general formula is that the nth shell can in principle hold up to 2 electrons, since electrons are electrically attracted to the nucleus, an atoms electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a requirement, atoms may have two or even three incomplete outer shells. For an explanation of why electrons exist in these shells see electron configuration, if the potential energy is set to zero at infinite distance from the atomic nucleus or molecule, the usual convention, then bound electron states have negative potential energy. If an atom, ion, or molecule is at the lowest possible level, it. If it is at an energy level, it is said to be excited. If more than one quantum state is at the same energy. They are then called degenerate energy levels, quantized energy levels result from the relation between a particles energy and its wavelength. For a confined particle such as an electron in an atom, only stationary states with energies corresponding to integral numbers of wavelengths can exist, for other states the waves interfere destructively, resulting in zero probability density. Elementary examples that show mathematically how energy levels come about are the particle in a box, the first evidence of quantization in atoms was the observation of spectral lines in light from the sun in the early 1800s by Joseph von Fraunhofer and William Hyde Wollaston. The notion of levels was proposed in 1913 by Danish physicist Niels Bohr in the Bohr theory of the atom. The modern quantum mechanical theory giving an explanation of these levels in terms of the Schrödinger equation was advanced by Erwin Schrödinger and Werner Heisenberg in 1926. When the electron is bound to the atom in any closer value of n, assume there is one electron in a given atomic orbital in a hydrogen-like atom
23.
Hadron
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In particle physics, a hadron /ˈhædrɒn/ is a composite particle made of quarks held together by the strong force in a similar way as molecules are held together by the electromagnetic force. Hadrons are categorized into two families, baryons, made of three quarks, and mesons, made of one quark and one antiquark, protons and neutrons are examples of baryons, pions are an example of a meson. Hadrons containing more than three valence quarks have been discovered in recent years, a tetraquark state, named the Z−, was discovered in 2007 by the Belle Collaboration and confirmed as a resonance in 2014 by the LHCb collaboration. Two pentaquark states, named P+ c and P+ c, were discovered in 2015 by the LHCb collaboration, there are several more exotic hadron candidates, and other colour-singlet quark combinations may also exist. Of the hadrons, protons are stable, and neutrons bound within atomic nuclei are stable, other hadrons are unstable under ordinary conditions, free neutrons decay with a half-life of about 611 seconds. Experimentally, hadron physics is studied by colliding protons or nuclei of elements such as lead. The term hadron was introduced by Lev B, okun in a plenary talk at the 1962 International Conference on High Energy Physics. In this talk he said, Notwithstanding the fact that this report deals with weak interactions and these particles pose not only numerous scientific problems, but also a terminological problem. The point is that strongly interacting particles is a very clumsy term which does not yield itself to the formation of an adjective, for this reason, to take but one instance, decays into strongly interacting particles are called non-leptonic. This definition is not exact because non-leptonic may also signify photonic, in this report I shall call strongly interacting particles hadrons, and the corresponding decays hadronic. I hope that this terminology will prove to be convenient, okun,1962 According to the quark model, the properties of hadrons are primarily determined by their so-called valence quarks. For example, a proton is composed of two up quarks and one down quark, adding these together yields the proton charge of +1. Although quarks also carry color charge, hadrons must have total color charge because of a phenomenon called color confinement. That is, hadrons must be colorless or white and these are the simplest of the two ways, three quarks of different colors, or a quark of one color and an antiquark carrying the corresponding anticolor. Hadrons with the first arrangement are called baryons, and those with the arrangement are mesons. Hadrons, however, are not composed of just three or two quarks, because of the strength of the strong force, more accurately, strong force gluons have enough energy to have resonances composed of massive quarks. Thus, virtual quarks and antiquarks, in a 1,1 ratio, the two or three quarks that compose a hadron are the excess of quarks vs. antiquarks, and so too in the case of anti-hadrons. Massless virtual gluons compose the majority of particles inside hadrons
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Meson
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In particle physics, mesons are hadronic subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of quark sub-particles, they have a size, with a diameter of roughly one fermi. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond, charged mesons decay to form electrons and neutrinos. Uncharged mesons may decay to photons, both of these decays imply that color is no longer a property of the byproducts. Outside of the nucleus, mesons appear in only as short-lived products of very high-energy collisions between particles made of quarks, such as cosmic rays and ordinary matter. Mesons are also frequently produced artificially in particle accelerators in the collisions of protons, anti-protons. Mesons are the associated quantum-field particles that transmit the force between hadrons that pull those together into a nucleus. Higher energy mesons were created momentarily in the Big Bang, but are not thought to play a role in nature today. However, such heavy mesons are regularly created in particle accelerator experiments, mesons are part of the hadron particle family, and are defined simply as particles composed of two quarks. The other members of the family are the baryons, subatomic particles composed of three quarks. Some experiments show evidence of exotic mesons, which do not have the conventional valence quark content of one quark, because quarks have a spin of 1⁄2, the difference in quark-number between mesons and baryons results in conventional two-quark mesons being bosons, whereas baryons are fermions. Each type of meson has a corresponding antiparticle in which quarks are replaced by their corresponding antiquarks and vice versa. For example, a pion is made of one up quark and one down antiquark, and its corresponding antiparticle. Because mesons are composed of quarks, they participate in both the weak and strong interactions, mesons with net electric charge also participate in the electromagnetic interaction. Mesons are classified according to their content, total angular momentum, parity and various other properties. Although no meson is stable, those of mass are nonetheless more stable than the more massive. Mesons are also less massive than baryons, meaning that they are more easily produced in experiments. For example, the quark was first seen in the J/Psi meson in 1974
25.
Baryon
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A baryon is a composite subatomic particle made up of three quarks. Baryons and mesons belong to the family of particles, which are the quark-based particles. The name baryon comes from the Greek word for heavy, because, at the time of their naming, as quark-based particles, baryons participate in the strong interaction, whereas leptons, which are not quark-based, do not. The most familiar baryons are the protons and neutrons that make up most of the mass of the matter in the universe. Each baryon has a corresponding antiparticle where quarks are replaced by their corresponding antiquarks, for example, a proton is made of two up quarks and one down quark, and its corresponding antiparticle, the antiproton, is made of two up antiquarks and one down antiquark. This is in contrast to the bosons, which do not obey the exclusion principle, Baryons, along with mesons, are hadrons, meaning they are particles composed of quarks. Quarks have baryon numbers of B = 1/3 and antiquarks have baryon number of B = −1/3, the term baryon usually refers to triquarks—baryons made of three quarks. Other exotic baryons have been proposed, such as made of four quarks and one antiquark. The particle physics community as a whole did not view their existence as likely in 2006, however, in July 2015, the LHCb experiment observed two resonances consistent with pentaquark states in the Λ0 b → J/ψK−p decay, with a combined statistical significance of 15σ. In theory, heptaquarks, nonaquarks, etc. could also exist, nearly all matter that may be encountered or experienced in everyday life is baryonic matter, which includes atoms of any sort, and provides those with the property of mass. Non-baryonic matter, as implied by the name, is any sort of matter that is not composed primarily of baryons and this might include neutrinos and free electrons, dark matter, such as supersymmetric particles, axions, and black holes. The very existence of baryons is also a significant issue in cosmology, the process by which baryons came to outnumber their antiparticles is called baryogenesis. Some grand unified theories of physics also predict that a single proton can decay, changing the baryon number by one, however. The excess of baryons over antibaryons in the present universe is thought to be due to non-conservation of baryon number in the early universe. The concept of isospin was first proposed by Werner Heisenberg in 1932 to explain the similarities between protons and neutrons under the strong interaction, although they had different electric charges, their masses were so similar that physicists believed they were the same particle. The different electric charges were explained as being the result of some unknown excitation similar to spin and this unknown excitation was later dubbed isospin by Eugene Wigner in 1937. This belief lasted until Murray Gell-Mann proposed the model in 1964. The success of the model is now understood to be the result of the similar masses of the u and d quarks
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Electroweak interaction
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In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature, electromagnetism and the weak interaction. Although these two forces appear very different at low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV, thus, if the universe is hot enough, then the electromagnetic force and weak force merge into a combined electroweak force. During the electroweak epoch, the electroweak force separated from the strong force, during the quark epoch, the electroweak force split into the electromagnetic and weak force. In 1999, Gerardus t Hooft and Martinus Veltman were awarded the Nobel prize for showing that the theory is renormalizable. Mathematically, the unification is accomplished under an SU × U gauge group, the corresponding gauge bosons are the three W bosons of weak isospin from SU, and the B boson of weak hypercharge from U, respectively, all of which are massless. In the Standard Model, the W± and Z0 bosons, UY and Uem are different copies of U, the generator of Uem is given by Q = Y/2 + I3, where Y is the generator of UY, and I3 is one of the SU generators. The spontaneous symmetry breaking makes the W3 and B bosons coalesce into two different bosons – the Z0 boson, and the photon, = Where θW is the mixing angle. The axes representing the particles have essentially just been rotated, in the plane and this also introduces a mismatch between the mass of the Z0 and the mass of the W± particles, M Z = M W cos θ W. The W1 and W2 bosons, in turn, combine to give massive charged bosons W ± =12, the Lagrangian for the electroweak interactions is divided into four parts before electroweak symmetry breaking L E W = L g + L f + L h + L y. The L g term describes the interaction between the three W particles and the B particle, L f is the kinetic term for the Standard Model fermions. The interaction of the bosons and the fermions are through the gauge covariant derivative. The h term describes the Higgs field F. L h = | D μ h |2 − λ2 The y term gives the Yukawa interaction that generates the masses after the Higgs acquires a nonzero vacuum expectation value. The Lagrangian reorganizes itself after the Higgs boson acquires a vacuum expectation value, due to its complexity, this Lagrangian is best described by breaking it up into several parts as follows. The neutral current L N and charged current L C components of the Lagrangian contain the interactions between the fermions and gauge bosons, the charged current part of the Lagrangian is given by L C = − g 2 W μ + + h. c. L H contains the Higgs three-point and four-point self interaction terms, L H = − g m H24 m W H3 − g 2 m H232 m W2 H4 L H V contains the Higgs interactions with gauge vector bosons. L H V = L W W V contains the gauge three-point self interactions. L Y = − ∑ f g m f 2 m W f ¯ f H Note the 1 − γ52 factors in the weak couplings and this is why electroweak theory is commonly said to be a chiral theory
27.
Strong interaction
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At the range of 10−15 m, the strong force is approximately 137 times as strong as electromagnetism, a million times as strong as the weak interaction and 1038 times as strong as gravitation. The strong nuclear force holds most ordinary matter together because it confines quarks into hadron particles such as proton and neutron, in addition, the strong force binds neutrons and protons to create atomic nuclei. Most of the mass of a proton or neutron is the result of the strong force field energy. The strong interaction is observable at two ranges, on a scale, it is the force that binds protons and neutrons together to form the nucleus of an atom. On the smaller scale, it is the force that holds together to form protons, neutrons. In the latter context, it is known as the color force. The strong force inherently has such a strength that hadrons bound by the strong force can produce new massive particles. Thus, if hadrons are struck by particles, they give rise to new hadrons instead of emitting freely moving radiation. This property of the force is called color confinement, and it prevents the free emission of the strong force, instead, in practice. In the context of binding protons and neutrons together to form atomic nuclei, in this case, it is the residuum of the strong interaction between the quarks that make up the protons and neutrons. As such, the strong interaction obeys a quite different distance-dependent behavior between nucleons, from when it is acting to bind quarks within nucleons. The binding energy that is released on the breakup of a nucleus is related to the residual strong force and is harnessed as fission energy in nuclear power. The strong interaction is mediated by the exchange of particles called gluons that act between quarks, antiquarks, and other gluons. Gluons are thought to interact with quarks and other gluons by way of a type of charge called color charge. Color charge is analogous to electromagnetic charge, but it comes in three rather than one, which results in a different type of force, with different rules of behavior. These rules are detailed in the theory of quantum chromodynamics, which is the theory of quark-gluon interactions, after the Big Bang and during the electroweak epoch of the universe, the electroweak force separated from the strong force. A Grand Unified Theory is hypothesized to exist to describe this, but no theory has yet been successfully formulated. Before the 1970s, physicists were uncertain as to how the nucleus was bound together
28.
Orthogonality
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The concept of orthogonality has been broadly generalized in mathematics, as well as in areas such as chemistry, and engineering. The word comes from the Greek ὀρθός, meaning upright, and γωνία, the ancient Greek ὀρθογώνιον orthogōnion and classical Latin orthogonium originally denoted a rectangle. Later, they came to mean a right triangle, in the 12th century, the post-classical Latin word orthogonalis came to mean a right angle or something related to a right angle. In geometry, two Euclidean vectors are orthogonal if they are perpendicular, i. e. they form a right angle, two vectors, x and y, in an inner product space, V, are orthogonal if their inner product ⟨ x, y ⟩ is zero. This relationship is denoted x ⊥ y, two vector subspaces, A and B, of an inner product space, V, are called orthogonal subspaces if each vector in A is orthogonal to each vector in B. The largest subspace of V that is orthogonal to a subspace is its orthogonal complement. Given a module M and its dual M∗, an element m′ of M∗, two sets S′ ⊆ M∗ and S ⊆ M are orthogonal if each element of S′ is orthogonal to each element of S. A term rewriting system is said to be if it is left-linear and is non-ambiguous. Orthogonal term rewriting systems are confluent, a set of vectors in an inner product space is called pairwise orthogonal if each pairing of them is orthogonal. Such a set is called an orthogonal set, nonzero pairwise orthogonal vectors are always linearly independent. In certain cases, the normal is used to mean orthogonal. For example, the y-axis is normal to the curve y = x2 at the origin, however, normal may also refer to the magnitude of a vector. In particular, a set is called if it is an orthogonal set of unit vectors. As a result, use of the normal to mean orthogonal is often avoided. The word normal also has a different meaning in probability and statistics, a vector space with a bilinear form generalizes the case of an inner product. When the bilinear form applied to two results in zero, then they are orthogonal. The case of a pseudo-Euclidean plane uses the term hyperbolic orthogonality, in the diagram, axes x′ and t′ are hyperbolic-orthogonal for any given ϕ. In 2-D or higher-dimensional Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i. e. they make an angle of 90°, hence orthogonality of vectors is an extension of the concept of perpendicular vectors into higher-dimensional spaces
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Determinant
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In linear algebra, the determinant is a useful value that can be computed from the elements of a square matrix. The determinant of a matrix A is denoted det, detA and it can be viewed as the scaling factor of the transformation described by the matrix. In the case of a 2 ×2 matrix, the formula for the determinant. Each determinant of a 2 ×2 matrix in this equation is called a minor of the matrix A, the same sort of procedure can be used to find the determinant of a 4 ×4 matrix, the determinant of a 5 ×5 matrix, and so forth. The use of determinants in calculus includes the Jacobian determinant in the change of rule for integrals of functions of several variables. Determinants are also used to define the characteristic polynomial of a matrix, in analytical geometry, determinants express the signed n-dimensional volumes of n-dimensional parallelepipeds. Sometimes, determinants are used merely as a notation for expressions that would otherwise be unwieldy to write down. When the entries of the matrix are taken from a field, it can be proven that any matrix has an inverse if. There are various equivalent ways to define the determinant of a square matrix A, i. e. one with the number of rows. Another way to define the determinant is expressed in terms of the columns of the matrix and these properties mean that the determinant is an alternating multilinear function of the columns that maps the identity matrix to the underlying unit scalar. These suffice to uniquely calculate the determinant of any square matrix, provided the underlying scalars form a field, the definition below shows that such a function exists, and it can be shown to be unique. Assume A is a matrix with n rows and n columns. The entries can be numbers or expressions, the definition of the determinant depends only on the fact that they can be added and multiplied together in a commutative manner. The determinant of a 2 ×2 matrix is defined by | a b c d | = a d − b c. If the matrix entries are numbers, the matrix A can be used to represent two linear maps, one that maps the standard basis vectors to the rows of A. In either case, the images of the vectors form a parallelogram that represents the image of the unit square under the mapping. The parallelogram defined by the rows of the matrix is the one with vertices at. The absolute value of ad − bc is the area of the parallelogram, the absolute value of the determinant together with the sign becomes the oriented area of the parallelogram
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Lie group
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In mathematics, a Lie group /ˈliː/ is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of transformation groups. The term groupes de Lie first appeared in French in 1893 in the thesis of Lie’s student Arthur Tresse, an extension of Galois theory to the case of continuous symmetry groups was one of Lies principal motivations. Lie groups are smooth manifolds and as such can be studied using differential calculus. Lie groups play an role in modern geometry, on several different levels. Felix Klein argued in his Erlangen program that one can consider various geometries by specifying an appropriate transformation group that leaves certain geometric properties invariant and this idea later led to the notion of a G-structure, where G is a Lie group of local symmetries of a manifold. On a global level, whenever a Lie group acts on an object, such as a Riemannian or a symplectic manifold. The presence of continuous symmetries expressed via a Lie group action on a manifold places strong constraints on its geometry, Linear actions of Lie groups are especially important, and are studied in representation theory. This insight opened new possibilities in pure algebra, by providing a uniform construction for most finite simple groups, a real Lie group is a group that is also a finite-dimensional real smooth manifold, in which the group operations of multiplication and inversion are smooth maps. Smoothness of the group multiplication μ, G × G → G μ = x y means that μ is a mapping of the product manifold G×G into G. These two requirements can be combined to the requirement that the mapping ↦ x −1 y be a smooth mapping of the product manifold into G. The 2×2 real invertible matrices form a group under multiplication, denoted by GL or by GL2 and this is a four-dimensional noncompact real Lie group. This group is disconnected, it has two connected components corresponding to the positive and negative values of the determinant, the rotation matrices form a subgroup of GL, denoted by SO. It is a Lie group in its own right, specifically, using the rotation angle φ as a parameter, this group can be parametrized as follows, SO =. Addition of the angles corresponds to multiplication of the elements of SO, thus both multiplication and inversion are differentiable maps. The orthogonal group also forms an example of a Lie group. All of the examples of Lie groups fall within the class of classical groups. Hilberts fifth problem asked whether replacing differentiable manifolds with topological or analytic ones can yield new examples, if the underlying manifold is allowed to be infinite-dimensional, then one arrives at the notion of an infinite-dimensional Lie group