1.
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

2.
Oxford University Press
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Oxford University Press is the largest university press in the world, and the second oldest after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the known as the delegates of the press. They are headed by the secretary to the delegates, who serves as OUPs chief executive, Oxford University has used a similar system to oversee OUP since the 17th century. The university became involved in the print trade around 1480, and grew into a printer of Bibles, prayer books. OUP took on the project became the Oxford English Dictionary in the late 19th century. Moves into international markets led to OUP opening its own offices outside the United Kingdom, by contracting out its printing and binding operations, the modern OUP publishes some 6,000 new titles around the world each year. OUP was first exempted from United States corporation tax in 1972, as a department of a charity, OUP is exempt from income tax and corporate tax in most countries, but may pay sales and other commercial taxes on its products. The OUP today transfers 30% of its surplus to the rest of the university. OUP is the largest university press in the world by the number of publications, publishing more than 6,000 new books every year, the Oxford University Press Museum is located on Great Clarendon Street, Oxford. Visits must be booked in advance and are led by a member of the archive staff, displays include a 19th-century printing press, the OUP buildings, and the printing and history of the Oxford Almanack, Alice in Wonderland and the Oxford English Dictionary. The first printer associated with Oxford University was Theoderic Rood, the first book printed in Oxford, in 1478, an edition of Rufinuss Expositio in symbolum apostolorum, was printed by another, anonymous, printer. Famously, this was mis-dated in Roman numerals as 1468, thus apparently pre-dating Caxton, roods printing included John Ankywylls Compendium totius grammaticae, which set new standards for teaching of Latin grammar. After Rood, printing connected with the university remained sporadic for over half a century, the chancellor, Robert Dudley, 1st Earl of Leicester, pleaded Oxfords case. Some royal assent was obtained, since the printer Joseph Barnes began work, Oxfords chancellor, Archbishop William Laud, consolidated the legal status of the universitys printing in the 1630s. Laud envisaged a unified press of world repute, Oxford would establish it on university property, govern its operations, employ its staff, determine its printed work, and benefit from its proceeds. To that end, he petitioned Charles I for rights that would enable Oxford to compete with the Stationers Company and the Kings Printer and these were brought together in Oxfords Great Charter in 1636, which gave the university the right to print all manner of books. Laud also obtained the privilege from the Crown of printing the King James or Authorized Version of Scripture at Oxford and this privilege created substantial returns in the next 250 years, although initially it was held in abeyance. The Stationers Company was deeply alarmed by the threat to its trade, under this, the Stationers paid an annual rent for the university not to exercise its full printing rights – money Oxford used to purchase new printing equipment for smaller purposes

3.
Quantum mechanics
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Quantum mechanics, including quantum field theory, is a branch of physics which is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, derives from quantum mechanics as an approximation valid only at large scales, early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms, in one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. In 1803, Thomas Young, an English polymath, performed the famous experiment that he later described in a paper titled On the nature of light. This experiment played a role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays, Plancks hypothesis that energy is radiated and absorbed in discrete quanta precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, ludwig Boltzmann independently arrived at this result by considerations of Maxwells equations. However, it was only at high frequencies and underestimated the radiance at low frequencies. Later, Planck corrected this model using Boltzmanns statistical interpretation of thermodynamics and proposed what is now called Plancks law, following Max Plancks solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. In 1913, Peter Debye extended Niels Bohrs theory of structure, introducing elliptical orbits. This phase is known as old quantum theory, according to Planck, each energy element is proportional to its frequency, E = h ν, where h is Plancks constant. Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right rather than a sizable discovery. He won the 1921 Nobel Prize in Physics for this work, lower energy/frequency means increased time and vice versa, photons of differing frequencies all deliver the same amount of action, but do so in varying time intervals. High frequency waves are damaging to human tissue because they deliver their action packets concentrated in time, the Copenhagen interpretation of Niels Bohr became widely accepted. In the mid-1920s, developments in mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory, out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons

4.
Fermion
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In particle physics, a fermion is any subatomic particle characterized by Fermi–Dirac statistics. These particles obey the Pauli exclusion principle, fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics, a fermion can be an elementary particle, such as the electron, or it can be a composite particle, such as the proton. According to the theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons. Besides this spin characteristic, fermions have another specific property, they possess conserved baryon or lepton quantum numbers, therefore, what is usually referred to as the spin statistics relation is in fact a spin statistics-quantum number relation. As a consequence of the Pauli exclusion principle, only one fermion can occupy a quantum state at any given time. If multiple fermions have the same probability distribution, then at least one property of each fermion, such as its spin. Weakly interacting fermions can also display bosonic behavior under extreme conditions, at low temperature fermions show superfluidity for uncharged particles and superconductivity for charged particles. Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter, the Standard Model recognizes two types of elementary fermions, quarks and leptons. In all, the model distinguishes 24 different fermions, there are six quarks, and six leptons, along with the corresponding antiparticle of each of these. Mathematically, fermions come in three types - Weyl fermions, Dirac fermions, and Majorana fermions, most Standard Model fermions are believed to be Dirac fermions, although it is unknown at this time whether the neutrinos are Dirac or Majorana fermions. Dirac fermions can be treated as a combination of two Weyl fermions, in July 2015, Weyl fermions have been experimentally realized in Weyl semimetals. Composite particles can be bosons or fermions depending on their constituents, more precisely, because of the relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion. Examples include the following, A baryon, such as the proton or neutron, the nucleus of a carbon-13 atom contains six protons and seven neutrons and is therefore a fermion. The atom helium-3 is made of two protons, one neutron, and two electrons, and therefore it is a fermion. The number of bosons within a composite made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion. Fermionic or bosonic behavior of a particle is only seen at large distances. At proximity, where spatial structure begins to be important, a composite particle behaves according to its constituent makeup, fermions can exhibit bosonic behavior when they become loosely bound in pairs

5.
Boson
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In quantum mechanics, a boson is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of particles, the other being fermions, an important characteristic of bosons is that their statistics do not restrict the number of them that occupy the same quantum state. This property is exemplified by helium-4 when it is cooled to become a superfluid, unlike bosons, two identical fermions cannot occupy the same quantum space. Whereas the elementary particles that make up matter are fermions, the elementary bosons are force carriers that function as the glue holding matter together and this property holds for all particles with integer spin as a consequence of the spin–statistics theorem. This state is called Bose-Einstein condensation and it is believed that this property is the explanation of superfluidity. Bosons may be elementary, like photons, or composite. If it exists, a graviton must be a boson, composite bosons are important in superfluidity and other applications of Bose–Einstein condensates. This phenomenon is known as Bose-Einstein condensation and it is believed that this phenomenon is the secret behind superfluidity of liquids, Bosons differ from fermions, which obey Fermi–Dirac statistics. Two or more identical fermions cannot occupy the same quantum state, since bosons with the same energy can occupy the same place in space, bosons are often force carrier particles. Fermions are usually associated with matter Bosons are particles which obey Bose–Einstein statistics, thus fermions are sometimes said to be the constituents of matter, while bosons are said to be the particles that transmit interactions, or the constituents of radiation. The quantum fields of bosons are bosonic fields, obeying canonical commutation relations, the properties of lasers and masers, superfluid helium-4 and Bose–Einstein condensates are all consequences of statistics of bosons. Interactions between elementary particles are called fundamental interactions, the fundamental interactions of virtual bosons with real particles result in all forces we know. All known elementary and composite particles are bosons or fermions, depending on their spin, particles with spin are fermions. In the framework of quantum mechanics, this is a purely empirical observation. However, in quantum field theory, the spin–statistics theorem shows that half-integer spin particles cannot be bosons. In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities—when their wave functions overlap, at low densities, both types of statistics are well approximated by Maxwell–Boltzmann statistics, which is described by classical mechanics. All observed elementary particles are fermions or bosons. The observed elementary bosons are all bosons, photons, W and Z bosons, gluons

6.
Commutative property
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In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says 3 +4 =4 +3 or 2 ×5 =5 ×2, the property can also be used in more advanced settings. The name is needed there are operations, such as division and subtraction. The commutative property is a property associated with binary operations and functions. If the commutative property holds for a pair of elements under a binary operation then the two elements are said to commute under that operation. The term commutative is used in several related senses, putting on socks resembles a commutative operation since which sock is put on first is unimportant. Either way, the result, is the same, in contrast, putting on underwear and trousers is not commutative. The commutativity of addition is observed when paying for an item with cash, regardless of the order the bills are handed over in, they always give the same total. The multiplication of numbers is commutative, since y z = z y for all y, z ∈ R For example,3 ×5 =5 ×3. Some binary truth functions are also commutative, since the tables for the functions are the same when one changes the order of the operands. For example, the logical biconditional function p ↔ q is equivalent to q ↔ p and this function is also written as p IFF q, or as p ≡ q, or as Epq. Further examples of binary operations include addition and multiplication of complex numbers, addition and scalar multiplication of vectors. Concatenation, the act of joining character strings together, is a noncommutative operation, rotating a book 90° around a vertical axis then 90° around a horizontal axis produces a different orientation than when the rotations are performed in the opposite order. The twists of the Rubiks Cube are noncommutative and this can be studied using group theory. Some non-commutative binary operations, Records of the use of the commutative property go back to ancient times. The Egyptians used the property of multiplication to simplify computing products. Euclid is known to have assumed the property of multiplication in his book Elements

7.
Parity (physics)
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In quantum mechanics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is often described by the simultaneous flip in the sign of all three spatial coordinates, P, ↦. It can also be thought of as a test for chirality of a physical phenomenon, a parity transformation on something achiral, on the other hand, can be viewed as an identity transformation. All fundamental interactions of particles, with the exception of the weak interaction, are symmetric under parity. The weak interaction is chiral and thus provides a means for probing chirality in physics, in interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions. A matrix representation of P has determinant equal to −1, and hence is distinct from a rotation, in a two-dimensional plane, a simultaneous flip of all coordinates in sign is not a parity transformation, it is the same as a 180°-rotation. Under rotations, classical geometrical objects can be classified into scalars, vectors, in classical physics, physical configurations need to transform under representations of every symmetry group. Quantum theory predicts that states in a Hilbert space do not need to transform under representations of the group of rotations, the projective representations of any group are isomorphic to the ordinary representations of a central extension of the group. For example, projective representations of the 3-dimensional rotation group, which is the orthogonal group SO, are ordinary representations of the special unitary group SU. Projective representations of the group that are not representations are called spinors. If one adds to this a classification by parity, these can be extended, for example, vectors and axial vectors which both transform as vectors under rotation. One can define reflections such as V x, ↦, which also have negative determinant, then, combining them with rotations one can recover the particular parity transformation defined earlier. The first parity transformation given does not work in an number of dimensions, though. In odd number of only the latter example of a parity transformation can be used. Parity forms the abelian group Z2 due to the relation P2 =1, all Abelian groups have only one-dimensional irreducible representations. For Z2, there are two representations, one is even under parity, the other is odd. These are useful in quantum mechanics, newtons equation of motion F = ma equates two vectors, and hence is invariant under parity. The law of gravity also involves only vectors and is also, therefore, however, angular momentum L is an axial vector, L = r × p, P = × = L

8.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker

9.
Involution (mathematics)
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In mathematics, an involution, or an involutory function, is a function f that is its own inverse, f = x for all x in the domain of f. The identity map is an example of an involution. Common examples in mathematics of nontrivial involutions include multiplication by −1 in arithmetic, other examples include circle inversion, rotation by a half-turn, and reciprocal ciphers such as the ROT13 transformation and the Beaufort polyalphabetic cipher. The number of involutions, including the identity involution, on a set with n =0,1,2. Elements is given by a recurrence relation found by Heinrich August Rothe in 1800, a0 = a1 =1, an = an −1 + an −2, for n >1. The first few terms of this sequence are 1,1,2,4,10,26,76,232, these numbers are called the telephone numbers, and they also count the number of Young tableaux with a given number of cells. The composition g ∘ f of two involutions f and g is an if and only if they commute, g ∘ f = f ∘ g. Every involution on an odd number of elements has at least one fixed point, more generally, for an involution on a finite set of elements, the number of elements and the number of fixed points have the same parity. Basic examples of involutions are the functions, f 1 = − x, or f 2 =1 x and these are not the only pre-calculus involutions. Another in R + is, f = ln , x >0, the graph of an involution is line-symmetric over the line y = x. This is due to the fact that the inverse of any general function will be its reflection over the 45° line y = x and this can be seen by swapping x with y. If, in particular, the function is an involution, then it will serve as its own reflection, other elementary involutions are useful in solving functional equations. A simple example of an involution of the three-dimensional Euclidean space is reflection against a plane, performing a reflection twice brings a point back to its original coordinates. Another is the reflection through the origin, this is an abuse of language as it is not a reflection. These transformations are examples of affine involutions, an involution is a projectivity of period 2, that is, a projectivity that interchanges pairs of points. Coxeter relates three theorems on involutions, Any projectivity that interchanges two points is an involution, the three pairs of opposite sides of a complete quadrangle meet any line in three pairs of an involution. If an involution has one fixed point, it has another, in this instance the involution is termed hyperbolic, while if there are no fixed points it is elliptic. Another type of involution occurring in geometry is a polarity which is a correlation of period 2

10.
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