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Vertex Function
In quantum electrodynamics, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory. In particular, it is the one particle irreducible correlation function involving the fermion \psi, the antifermion \bar, and the vector potential A. Definition The vertex function \Gamma^\mu can be defined in terms of a functional derivative of the effective action Seff as :\Gamma^\mu = - The dominant (and classical) contribution to \Gamma^\mu is the gamma matrix \gamma^\mu, which explains the choice of the letter. The vertex function is constrained by the symmetries of quantum electrodynamics — Lorentz invariance; gauge invariance or the transversality of the photon, as expressed by the Ward identity; and invariance under parity — to take the following form: : \Gamma^\mu = \gamma^\mu F_1(q^2) + \frac F_2(q^2) where \sigma^ = (i/2) gamma^, \gamma^, q_ is the incoming four-momentum of the external photon (on the rig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen. History The first formulation of a quantum theory describing radiation and matter interaction is attributed to British scientist Paul Dirac, who ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Invariance
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations ( Lie groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the '' symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called '' gauge bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiley-VCH
Wiley-VCH is a German publisher owned by John Wiley & Sons. It was founded in 1921 as Verlag Chemie (meaning "Chemistry Press": VCH stands for ''Verlag Chemie'') by two German learned societies. Later, it was merged into the German Chemical Society (GDCh). In 1991, VCH acquired Akademie Verlag :''There also were unrelated publishing houses in Stuttgart and in (East-)Berlin, and there is the (JAVG).'' Akademie Verlag (AV) is a German scientific and academic publishing company, founded in 1946 in the Soviet-occupied eastern part .... It has been owned by John Wiley & Sons since 1996. The humanities section of Akademie Verlag and the Akademie brand were sold in 1997 to R. Oldenbourg Verlag, while VCH retained the natural sciences catalog. References External links * Wiley (publisher) Publishing companies of Germany Publishing companies established in 1921 Weinheim German companies established in 1921 {{publish-company-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landé G-factor
In physics, the Landé ''g''-factor is a particular example of a ''g''-factor, namely for an electron with both spin and orbital angular momenta. It is named after Alfred Landé, who first described it in 1921. In atomic physics, the Landé ''g''-factor is a multiplicative term appearing in the expression for the energy levels of an atom in a weak magnetic field. The quantum states of electrons in atomic orbitals are normally degenerate in energy, with these degenerate states all sharing the same angular momentum. When the atom is placed in a weak magnetic field, however, the degeneracy is lifted. Description The factor comes about during the calculation of the first-order perturbation in the energy of an atom when a weak uniform magnetic field (that is, weak in comparison to the system's internal magnetic field) is applied to the system. Formally we can write the factor as, :g_J= g_L\frac+g_S\frac. The orbital g_L is equal to 1, and under the approximation g_S = 2 , the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anomalous Magnetic Moment
In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. (The ''magnetic moment'', also called ''magnetic dipole moment'', is a measure of the strength of a magnetic source.) The "Dirac" magnetic moment, corresponding to tree-level Feynman diagrams (which can be thought of as the classical result), can be calculated from the Dirac equation. It is usually expressed in terms of the ''g''-factor; the Dirac equation predicts g = 2. For particles such as the electron, this classical result differs from the observed value by a small fraction of a percent. The difference is the anomalous magnetic moment, denoted a and defined as a = \frac Electron The one-loop contribution to the anomalous magnetic moment—corresponding to the first and largest quantum mechanical correction—of the electron is found by calculating the vertex functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field Strength Renormalization
Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grassland that is either natural or allowed to grow unmowed and ungrazed * Playing field, used for sports or games Arts and media * In decorative art, the main area of a decorated zone, often contained within a border, often the background for motifs ** Field (heraldry), the background of a shield ** In flag terminology, the background of a flag * ''FIELD'' (magazine), a literary magazine published by Oberlin College in Oberlin, Ohio * ''Field'' (sculpture), by Anthony Gormley Organizations * Field department, the division of a political campaign tasked with organizing local volunteers and directly contacting voters * Field Enterprises, a defunct private holding company ** Field Communications, a division of Field Enterprises * Field Mus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Form Factor (quantum Field Theory)
In elementary particle physics and mathematical physics, in particular in effective field theory, a form factor is a function that encapsulates the properties of a certain particle interaction without including all of the underlying physics, but instead, providing the momentum dependence of suitable matrix elements. It is further measured experimentally in confirmation or specification of a theory—see experimental particle physics. Photon–nucleon example For example, at low energies the interaction of a photon with a nucleon is a very complicated calculation involving interactions between the photon and a sea of quarks and gluons, and often the calculation cannot be fully performed from first principles. Often in this context, form factors are also called "structure functions", since they can be used to describe the structure of the nucleon. However, the generic Lorentz-invariant form of the matrix element for the electromagnetic current interaction is known, : \varepsilo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (physics)
In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection): :\mathbf: \beginx\\y\\z\end \mapsto \begin-x\\-y\\-z\end. It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. All fundamental interactions of elementary 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 (in any number of dimensions) has determinant equal to −1, and hence is distinct from a rotat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ward Identity
Ward may refer to: Division or unit * Hospital ward, a hospital division, floor, or room set aside for a particular class or group of patients, for example the psychiatric ward * Prison ward, a division of a penal institution such as a prison * Ward (electoral subdivision), electoral district or unit of local government ** Ward (KPK), local government in Khyber Pakhtunkhwa, Pakistan ** Ward (South Africa) ** Wards of Bangladesh ** Wards of Germany ** Wards of Japan ** Wards of Myanmar ** Wards and electoral divisions of the United Kingdom ** Ward (United States) *** Wards of New Orleans * Ward (fortification), part of a castle * Ward (LDS Church), a local congregation of The Church of Jesus Christ of Latter-day Saints * Ward (Vietnam), a type of third-tier subdivision of Vietnam Entertainment, arts and media * WOUF (AM), a radio station (750 AM) licensed to serve Petoskey, Michigan, United States, which held the call sign WARD from 2008 to 2021 * Ward Cleaver, a fictional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photon Polarization
Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization, or a superposition of the two. Equivalently, a photon can be described as having horizontal or vertical linear polarization, or a superposition of the two. The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well. Polarization is an example of a qubit degree of freedom, which forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description. The quantum polarization state v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Invariance
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of vectors, or from contracting tensors of the theory. While the components of vectors and tensors are in general altered under Lorentz transformations, Lorentz scalars remain unchanged. A Lorentz scalar is not always immediately seen to be an invariant scalar in the mathematical sense, but the resulting scalar value is invariant under any basis transformation applied to the vector space, on which the considered theory is based. A simple Lorentz scalar in Minkowski spacetime is the ''spacetime distance'' ("length" of their difference) of two fixed events in spacetime. While the "position"-4-vectors of the events change between different inertial frames, their spacetime distance remains invariant under the corresponding Lorentz transformation. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
