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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.
Supersymmetry
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Each particle from one group is associated with a particle from the other, known as its superpartner, the spin of which differs by a half-integer. In a theory with perfectly unbroken supersymmetry, each pair of superpartners would share the same mass, for example, there would be a selectron, a bosonic version of the electron with the same mass as the electron, that would be easy to find in a laboratory. Thus, since no superpartners have been observed, if supersymmetry exists it must be a broken symmetry so that superpartners may differ in mass. Spontaneously-broken supersymmetry could solve many problems in particle physics including the hierarchy problem. The simplest realization of spontaneously-broken supersymmetry, the so-called Minimal Supersymmetric Standard Model, is one of the best studied candidates for physics beyond the Standard Model, there is only indirect evidence and motivation for the existence of supersymmetry. Direct confirmation would entail production of superpartners in collider experiments, such as the Large Hadron Collider, the first run of the LHC found no evidence for supersymmetry, and thus set limits on superpartner masses in supersymmetric theories. While some remain enthusiastic about supersymmetry, this first run at the LHC led some physicists to explore other ideas, the LHC resumed its search for supersymmetry and other new physics in its second run. There are numerous phenomenological motivations for supersymmetry close to the electroweak scale, supersymmetry close to the electroweak scale ameliorates the hierarchy problem that afflicts the Standard Model. In the Standard Model, the electroweak scale receives enormous Planck-scale quantum corrections, the observed hierarchy between the electroweak scale and the Planck scale must be achieved with extraordinary fine tuning. In a supersymmetric theory, on the hand, Planck-scale quantum corrections cancel between partners and superpartners. The hierarchy between the scale and the Planck scale is achieved in a natural manner, without miraculous fine-tuning. The idea that the symmetry groups unify at high-energy is called Grand unification theory. In the Standard Model, however, the weak, strong, in a supersymmetry theory, the running of the gauge couplings are modified, and precise high-energy unification of the gauge couplings is achieved. The modified running also provides a mechanism for radiative electroweak symmetry breaking. TeV-scale supersymmetry typically provides a dark matter particle at a mass scale consistent with thermal relic abundance calculations. Supersymmetry is also motivated by solutions to several problems, for generally providing many desirable mathematical properties. Supersymmetric quantum field theory is much easier to analyze, as many more problems become exactly solvable. When supersymmetry is imposed as a symmetry, Einsteins theory of general relativity is included automatically

3.
Spontaneous symmetry breaking
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Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetrical state ends up in an asymmetrical state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, in explicit symmetry breaking, if we consider two outcomes, the probability of a pair of outcomes can be different. By definition, spontaneous symmetry breaking requires the existence of a symmetrical probability distribution--any pair of outcomes has the same probability, in other words, the underlying laws are invariant under a symmetry transformation. The system as a whole changes under such transformations, phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the fractional quantum Hall effect, consider a symmetrical upward dome with a trough circling the bottom. If a ball is put at the peak of the dome. But the ball may spontaneously break this symmetry by rolling down the dome into the trough, afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not, in the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative scalar field theory. The relevant Lagrangian, which dictates how a system behaves, can be split up into kinetic and potential terms. An example of a potential, due to Jeffrey Goldstone is illustrated in the graph at the right and this potential has an infinite number of possible minima given by for any real θ between 0 and 2π. The system also has a vacuum state corresponding to Φ =0. This state has a U symmetry, however, once the system falls into a specific stable vacuum state, this symmetry will appear to be lost, or spontaneously broken. For ferromagnetic materials, the laws are invariant under spatial rotations. Here, the parameter is the magnetization, which measures the magnetic dipole density. Above the Curie temperature, the parameter is zero, which is spatially invariant. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, the residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken. The laws describing a solid are invariant under the full Euclidean group, the displacement and the orientation are the order parameters. Similar comments can be made about the microwave background

4.
Higgs mechanism
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In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property mass for gauge bosons. Without the Higgs mechanism, all bosons would be massless, but measurements show that the W+, W−, the Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field that permeates all space, below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass, in the Standard Model, the phrase Higgs mechanism refers specifically to the generation of masses for the W±, and Z weak gauge bosons through electroweak symmetry breaking. The Higgs mechanism was incorporated into modern particle physics by Steven Weinberg and Abdus Salam, in the standard model, at temperatures high enough that electroweak symmetry is unbroken, all elementary particles are massless. At a critical temperature, the Higgs field becomes tachyonic, the symmetry is broken by condensation. Fermions, such as the leptons and quarks in the Standard Model, can acquire mass as a result of their interaction with the Higgs field. In the standard model, the Higgs field is an SU doublet, the Higgs field, through the interactions specified by its potential, induces spontaneous breaking of three out of the four generators of the gauge group U. This is often written as SU × U, because the phase factor also acts on other fields in particular quarks. Three out of its four components would ordinarily amount to Goldstone bosons, the gauge group of the electroweak part of the standard model is SU × U. The group SU is the group of all 2-by-2 unitary matrices with unit determinant, rotating the coordinates so that the second basis vector points in the direction of the Higgs boson makes the vacuum expectation value of H the spinor. The generators for rotations about the x, y, and z axes are by half the Pauli matrices σx, σy, while the Tx and Ty generators mix up the top and bottom components of the spinor, the Tz rotations only multiply each by opposite phases. This phase can be undone by a U rotation of angle 1/2θ, consequently, under both an SU Tz-rotation and a U rotation by an amount 1/2θ, the vacuum is invariant. This combination of generators preserves the vacuum, and defines the unbroken gauge group in the standard model, the part of the gauge field in this direction stays massless, and amounts to the physical photon. In spite of the introduction of spontaneous symmetry breaking, the mass terms preclude chiral gauge invariance, for these fields the mass terms should always be replaced by a gauge-invariant Higgs mechanism. The quantities γμ are the Dirac matrices, and Gψ is the already-mentioned Yukawa coupling parameter, already now the mass-generation follows the same principle as above, namely from the existence of a finite expectation value | ⟨ ϕ ⟩ |, as described above. Again, this is crucial for the existence of the property mass, spontaneous symmetry breaking offered a framework to introduce bosons into relativistic quantum field theories. However, according to Goldstones theorem, these bosons should be massless, the only observed particles which could be approximately interpreted as Goldstone bosons were the pions, which Yoichiro Nambu related to chiral symmetry breaking

5.
Chaos theory
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Chaos theory is a branch of mathematics focused on the behavior of dynamical systems that are highly sensitive to initial conditions. This happens even though these systems are deterministic, meaning that their behavior is fully determined by their initial conditions. In other words, the nature of these systems does not make them predictable. This behavior is known as chaos, or simply chaos. The theory was summarized by Edward Lorenz as, Chaos, When the present determines the future, Chaotic behavior exists in many natural systems, such as weather and climate. It also occurs spontaneously in some systems with components, such as road traffic. This behavior can be studied through analysis of a mathematical model, or through analytical techniques such as recurrence plots. Chaos theory has applications in several disciplines, including meteorology, sociology, physics, environmental science, computer science, engineering, economics, biology, ecology, the theory formed the basis for such fields of study as complex dynamical systems, edge of chaos theory, self-assembly process. Chaos theory concerns deterministic systems whose behavior can in principle be predicted, Chaotic systems are predictable for a while and then appear to become random. Some examples of Lyapunov times are, chaotic electrical circuits, about 1 millisecond, weather systems, a few days, in chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast and this means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When meaningful predictions cannot be made, the system appears random, in common usage, chaos means a state of disorder. However, in theory, the term is defined more precisely. Although no universally accepted mathematical definition of chaos exists, a commonly used definition originally formulated by Robert L, in these cases, while it is often the most practically significant property, sensitivity to initial conditions need not be stated in the definition. If attention is restricted to intervals, the second property implies the other two, an alternative, and in general weaker, definition of chaos uses only the first two properties in the above list. Sensitivity to initial conditions means that each point in a system is arbitrarily closely approximated by other points with significantly different future paths. Thus, a small change, or perturbation, of the current trajectory may lead to significantly different future behavior. C. Entitled Predictability, Does the Flap of a Butterflys Wings in Brazil set off a Tornado in Texas, the flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena