In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom. This article needs additional references or sources for verification. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... The magnitude of an electric field surrounding two equally charged (repelling) particles. ... In mathematics, a local field is a special type of field which has the additional property that it is a complete metric space with respect to a discrete valuation. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Symmetry is a characteristic of geometrical shapes, equations and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ...

Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration by a particular detailed configuration (or even a weighted distribution of them). Judicious gauge fixing can simplify calculations immensely, but becomes progressively harder as the physical model becomes more realistic; its application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically, the search for logically consistent and computationally tractable gauge fixing procedures, and efforts to demonstrate their equivalence in the face of a bewildering variety of technical difficulties, has been a major driver of mathematical physics from the late nineteenth century to the present. Quantum field theory (QFT) is the quantum theory of fields. ... Figure 1. ... In quantum mechanics, perturbation theory is a set of approximation schemes for describing a complicated quantum system in terms of a simpler one. ... Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories. ...

Gauge freedom

The archetypical gauge theory is the Heaviside-Gibbs formulation of continuum electrodynamics in terms of an electromagnetic four-potential, which is presented here in space/time asymmetric Heaviside notation. The electric field and magnetic flux density of Maxwell's equations contain only "physical" degrees of freedom, in the sense that every mathematical degree of freedom in an electromagnetic field configuration has a separately measurable effect on the motions of test charges in the vicinity. These "field strength" variables can be expressed in terms of the scalar potential and the vector potential through the relations: Oliver Heaviside (May 18, 1850 – February 3, 1925) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, developed techniques for applying Laplace transforms to the solution of differential equations, reformulated Maxwells field equations in terms of electric and... Josiah Willard Gibbs (February 11, 1839 New Haven – April 28, 1903 New Haven) was one of the very first American theoretical physicists and chemists. ... Electromagnetic potential is . ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... Current flowing through a wire produces a magnetic field (B, labeled M here) around the wire. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... This article does not cite any references or sources. ... In physics, the magnetic potential is a method of representing the magnetic field by using a potential value instead of the actual vector field. ...

 and 

However, the and fields are unchanged if we take any function and transform and via:

A particular choice of the scalar and vector potentials is a gauge, and a scalar function ψ used to change the gauge is called a gauge function. The existence of arbitrary numbers of gauge functions , corresponds to the U(1) gauge freedom of this theory. Gauge fixing can be done in many ways, some of which we exhibit below. In mathematics, the unitary group of degree n, denoted U(n), is the group of n×n unitary matrices, with the group operation that of matrix multiplication. ...

Although classical electromagnetism is now often spoken of as a gauge theory, it was not originally conceived in these terms. The motion of a classical point charge is affected only by the electric and magnetic field strengths at that point, and the potentials can be treated as a mere mathematical device for simplifying some proofs and calculations. Not until the advent of quantum field theory could it be said that the potentials themselves are part of the physical configuration of a system. The earliest consequence to be accurately predicted and experimentally verified was the Aharonov-Bohm effect, which has no classical counterpart. The Aharonov-Bohm effect, sometimes called the Ehrenberg-Siday-Aharonov-Bohm effect, is a quantum mechanical phenomenon by which a charged particle is affected by electromagnetic fields in regions from which the particle is excluded. ...

Gauge fixing in non-abelian gauge theories, such as Yang-Mills theory and general relativity, is a rather more complicated topic; for details see Gribov ambiguity, Faddeev-Popov ghost, and frame bundle. In mathematics, an abelian group, also called a commutative group, is a group (G, *) such that a * b = b * a for all a and b in G. Abelian groups are named after Niels Henrik Abel. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... An illustration of a rotating black hole at the center of a galaxy General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... In gauge theory, especially nonAbelian gauge theories, we often encounter global problems when gauge fixing. ... In physics, Faddeev-Popov ghost ci is a field that violates the spin-statistics relation. ... In mathematics, the idea of a frame in the theory of smooth manifolds is understood in terms meaning it can vary from point to point. ...

An illustration

Gauge fixing of a twisted cylinder. (Note: the line is on the surface of the cylinder, not inside it.)

By looking at a cylindrical rod can one tell whether it is twisted? If the rod is perfectly cylindrical, then the circular symmetry of the cross section makes it impossible to give an answer. However, if there were a straight line drawn along the length of the rod, then one could easily say whether or not there is a twist by looking at the state of the line. Drawing a line is gauge fixing. Drawing the line spoils the gauge symmetry, ie, the circular symmetry U(1) of the cross section at each point of the rod. The line is the equivalent of a gauge function; it need not be straight. Almost any line is a valid gauge fixing, ie, there is a large gauge freedom. To tell whether the rod is twisted, you need to first know the gauge. Physical quantities, such as the energy of the torsion do not depend on the gauge, ie, they are gauge invariant. Image File history File links Cylinder and gauge line File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Cylinder and gauge line File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... In mathematics, the unitary group of degree n, denoted U(n), is the group of n×n unitary matrices, with the group operation that of matrix multiplication. ...

Coulomb gauge

The Coulomb gauge (also known as transverse or radiation gauge) is given by the constraint

In the Coulomb gauge, it can be seen from Gauss' law that the scalar potential is determined simply by Poisson's equation based on the total charge density ρ (including bound charge): In physics, Gausss law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. ... In mathematics, Poissons equation is a partial differential equation with broad utility in electrostatics, mechanical engineering and theoretical physics. ... In classical electromagnetism, the polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. ...

The solution to this equation is the instantaneous Coulomb potential associated with the charge density, which appears at first glance to violate causality, since motions of electric charge appear everywhere instantaneously as changes to the Coulomb potential. This is generally explained by pointing out that the scalar and vector potentials themselves do not affect the motions of charges, only the combinations of their derivatives that form the electromagnetic field strength. Although one can compute the field strengths explicitly in Coulomb gauge and demonstrate that changes in them propagate at the speed of light, it is much simpler to observe that the field strengths are unchanged under gauge transformations and to demonstrate causality in the manifestly covariant Lorenz gauge described below. It has been suggested that this article be split into multiple articles accessible from a disambiguation page. ...

The advantage of the Coulomb gauge is that one can decouple the equations for the scalar and vector potentials, obtaining a wave equation for the vector potential in terms of a quantity called the transverse current which, like the Coulomb potential, drops rapidly to zero outside the immediate vicinity of electric charges. Solutions of this wave equation with the transverse current set to zero correspond classically to transversely polarized electromagnetic radiation in free space. This is particularly useful for "semi-classical" calculations in quantum mechanics, in which the vector potential is quantized but the Coulomb interaction is not. The wave equation is an important partial differential equation that describes the propagation of a variety of waves, such as sound waves, light waves and water waves. ... Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. ... Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. ...

Lorenz gauge

The Lorenz gauge is given, in SI units, by: Look up si, Si, SI in Wiktionary, the free dictionary. ...

and in Gaussian units by: CGS is an acronym for centimetre-gram-second. ...

It may be rewritten in terms of the electromagnetic four-potential: Electromagnetic potential is . ...

It is unique among the constraint gauges in retaining manifest Lorentz invariance. Note, however, that this gauge was originally named after the Danish physicist Ludvig Lorenz and not after Hendrik Lorentz; it is often misspelled "Lorentz gauge". (Neither was the first to use it in calculations; it was introduced in 1888 by George F. Fitzgerald.) Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ... Ludvig Valentin Lorenz (1829 - 1891) was a Danish mathematician and physicist. ... Hendrik Antoon Lorentz (July 18, 1853, Arnhem – February 4, 1928, Haarlem) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and elucidation of the Zeeman effect. ... George FitzGerald George Francis FitzGerald, or Fitzgerald, (3 August 1851 - 22 February 1901) was a professor of natural and experimental philosophy (i. ...

The Lorenz gauge leads two the following inhomogeneous wave equations for the potentials:

It can be seen from these equations that, in the absence of current and charge, the solutions are potentials which propagate at the speed of light.

The Lorenz gauge is incomplete in the sense that there remains a subspace of gauge transformations which preserve the constraint. These remaining degrees of freedom correspond to gauge functions which satisfy the wave equation The wave equation is an important partial differential equation that describes the propagation of a variety of waves, such as sound waves, light waves and water waves. ...

These remaining gauge degrees of freedom propagate at the speed of light. To obtain a fully fixed gauge, one must add boundary conditions along the light cone of the experimental region. In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. ...

Maxwell's equations in the Lorenz gauge simplify to , where j^ν is the electromagnetic current. Two solutions of these equations for the same current configuration differ by a solution of the vacuum wave equation . In this form it is clear that the components of the potential separately satisfy the Klein-Gordon equation, and hence that the Lorenz gauge condition allows transversely, longitudinally, and "time-like" polarized waves in the four-potential. The transverse polarizations correspond to classical radiation, i. e., transversely polarized waves in the field strength. To suppress the "unphysical" longitudinal and time-like polarization states, which are not observed in experiments at classical distance scales, one must also employ auxiliary constraints known as Ward identities. Classically, these identities are equivalent to the current conservation constraint . The Klein-Gordon equation (Klein-Fock-Gordon equation or sometimes Klein-Gordon-Fock equation) is the relativistic version of the Schrödinger equation. ... This article treats polarization in electrodynamics. ... This article is about a formulation of quantum mechanics. ...

Many of the differences between classical and quantum electrodynamics can be accounted for by the role that the longitudinal and time-like polarizations play in interactions between charged particles at microscopic distances. This was not well understood at first even by active researchers in the field^[1] and remains inconspicuous in most textbook treatments, partly because a rigorous derivation of the photon propagator requires deeper mathematical tools than one needs for the rest of QED.^{[citation needed]}. Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ...

R_ξ gauges

The R_ξ gauges are a generalization of the Lorenz gauge applicable to theories expressed in terms of an action principle with Lagrangian density . Instead of fixing the gauge by constraining the gauge field a priori via an auxiliary equation, one adds to the "physical" (gauge invariant) Lagrangian a gauge breaking term A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a functional of the dynamical variables which concisely describes the equations of motion of the system. ...

The choice of the parameter ξ determines the choice of gauge. The Landau gauge, obtained as the limit , is classically equivalent to Lorenz gauge, but postponing taking the limit until after the theory is quantized improves the rigor of certain existence and equivalence proofs. Most quantum field theory computations are simplest in the Feynman-'t Hooft gauge, in which ξ = 1; a few are more tractable in other R_ξ gauges, such as the Yennie gauge ξ = 3. Quantum field theory (QFT) is the quantum theory of fields. ...

An equivalent formulation of R_ξ gauge uses an auxiliary field, a scalar field B with no independent dynamics: This article does not cite any references or sources. ...

The auxiliary field can be eliminated by "completing the square" to obtain the previous form. From a mathematical perspective the auxiliary field is a variety of Goldstone boson, and its use has advantages when identifying the asymptotic states of the theory, and especially when generalizing beyond QED. In particle and condensed matter physics, Goldstone bosons (also known as Nambu-Goldstone bosons) are bosons that appear in models with spontaneously broken symmetry. ...

Historically, the use of R_ξ gauges was a significant technical advance in extending quantum electrodynamics computations beyond one-loop order. In addition to retaining manifest Lorentz invariance, the R_ξ prescription breaks the symmetry under local gauge transformations while preserving the ratio of functional measures of any two physically distinct gauge configurations. This permits a change of variables in which infinitesimal perturbations along "physical" directions in configuration space are entirely uncoupled from those along "unphysical" directions, allowing the latter to be absorbed into the physically meaningless normalization of the functional integral. When ξ is finite, each physical configuration (orbit of the group of gauge transformations) is represented not by a single solution of a constraint equation but by a Gaussian distribution centered on the extremum of the gauge breaking term. In terms of the Feynman rules of the gauge-fixed theory, this appears as a contribution to the photon propagator for internal lines from virtual photons of unphysical polarization. Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic). ... Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ... In calculus, the substitution rule is a tool for finding antiderivatives and integrals. ... Broadly, normalization (also spelled normalisation) is any process that makes something more normal, which typically means conforming to some regularity or rule, or returning from some state of abnormality. ... In physics, functional integration is integration over certain infinite-dimensional spaces. ... In mathematics, particularly in calculus, a stationary point is a point on the graph of a function where the tangent to the graph is parallel to the x-axis or, equivalently, where the derivative of the function equals zero (known as a critical number). ... This page is a candidate for speedy deletion. ... In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... In electrodynamics, polarization (also spelled polarisation) is the property of electromagnetic waves, such as light, that describes the direction of their transverse electric field. ...

The photon propagator, which is the multiplicative factor corresponding to an internal photon in the Feynman diagram expansion of a QED calculation, contains a factor g_μν corresponding to the Minkowski metric. An expansion of this factor as a sum over photon polarizations involves terms containing all four possible polarizations. Transversely polarized radiation can be expressed mathematically as a sum over either a linearly or circularly polarized basis. Similarly, one can combine the longitudinal and time-like gauge polarizations to obtain "forward" and "backward" polarizations; these are a form of light cone coordinates in which the metric is off-diagonal. An expansion of the g_μν factor in terms of circularly polarized (spin +/- 1) and light cone coordinates is called a spin sum. Spin sums can be very helpful both in simplifying expressions and in obtaining a physical understanding of the experimental effects associated with different terms in a theoretical calculation. In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... In electrodynamics, circular polarization (also circular polarisation) of electromagnetic radiation is a polarization such that the tip of the electric field vector, at a fixed point in space, describes a circle as time progresses. ...

Richard Feynman used arguments along approximately these lines largely to justify calculation procedures that produced consistent, finite, high precision results for important observable parameters such as the anomalous magnetic moment of the electron. Although his arguments sometimes lacked mathematical rigor even by physicists' standards and glossed over details such as the derivation of Ward-Takahashi identities of the quantum theory, his calculations worked, and Freeman Dyson soon demonstrated that his method was substantially equivalent to those of Julian Schwinger and Sin-Itiro Tomonaga, with whom Feynman shared the 1965 Nobel Prize in Physics. Richard Phillips Feynman (May 11, 1918 – February 15, 1988; IPA: ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ... In quantum electrodynamics, 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. ... This article is about a formulation of quantum mechanics. ... Freeman John Dyson (born December 15, 1923) is a British-born American physicist and mathematician, famous for his work in quantum mechanics, solid-state physics, nuclear weapons design and policy, and for his serious theorizing in futurism and science fiction concepts, including the search for extraterrestrial intelligence. ... Julian Seymour Schwinger (February 12, 1918 -- July 16, 1994) was an American theoretical physicist. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Year 1965 (MCMLXV) was a common year starting on Friday (link will display full calendar) of the 1965 Gregorian calendar. ... Nobel Prize medal. ...

Forward and backward polarized radiation can be omitted in the asymptotic states of a quantum field theory (see Ward-Takahashi identity). For this reason, and because their appearance in spin sums can be seen as a mere mathematical device in QED (much like the electromagnetic four-potential in classical electrodynamics), they are often spoken of as "unphysical". But unlike the constraint-based gauge fixing procedures above, the R_ξ gauge generalizes well to non-abelian gauge groups such as the SU(3) of QCD. The couplings between physical and unphysical perturbation axes do not entirely disappear under the corresponding change of variables; to obtain correct results, one must account for the non-trivial Jacobian of the embedding of gauge freedom axes within the space of detailed configurations. This leads to the explicit appearance of forward and backward polarized gauge bosons in Feynman diagrams, along with Faddeev-Popov ghosts, which are even more "unphysical" in that they violate the spin-statistics theorem. The relationship between these entities, and the reasons why they do not appear as particles in the quantum mechanical sense, becomes more evident in the BRST formalism of quantization. In quantum field theory a Ward-Takahashi identity is nowadays used to designate an identity between correlation functions that follows from symmetries, either global or gauged, of the theory, and which remains valid after renormalization. ... In mathematics, an abelian group, also called a commutative group, is a group (G, *) such that a * b = b * a for all a and b in G. Abelian groups are named after Niels Henrik Abel. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... The initialism QCD can mean: Quantum chromodynamics Quintessential Player, formerly known as Quintessential CD Quality, Cost, Delivery, A three-letter acronym used in lean manufacturing This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... In vector calculus, the Jacobian is shorthand for either the Jacobian matrix or its determinant, the Jacobian determinant. ... In physics, Faddeev-Popov ghost ci is a field that violates the spin-statistics relation. ... The spin-statistics theorem in quantum mechanics relates the spin of a particle to the statistics obeyed by that particle. ... In physics, a particle is an object, or body, with only a few degrees-of-freedom, including position, and perhaps orientation in space. ... In theoretical physics, the BRST formalism is a method of implementing first class constraints. ...

Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... e- redirects here. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... In theoretical physics, a particles self-energy represents the contribution to the particles energy or effective mass due to interactions between the particle and the system it is apart of. ... In quantum physics, if we expand about the Fock vacuum, the true vacuum contains short-lived virtual particle-antiparticle pairs which are created in pairs out of the Fock vacuum and then annihilate each other. ... In quantum electrodynamics, the vertex function is the one particle irreducible correlation function involving ψ, and the vector potential A. It is unfortunate that the effective action Γeff and the vertex function Γμ happen to be described by the same letter. ... In quantum field theory, the Gupta-Bleuler formalism is a way of quantizing the electromagnetic field. ... In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. ... In quantum field theory a Ward-Takahashi identity is nowadays used to designate an identity between correlation functions that follows from symmetries, either global or gauged, of the theory, and which remains valid after renormalization. ... In physics, Compton scattering or the Compton effect, is the decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, when it interacts with matter. ... In quantum electrodynamics, Bhabha scattering is the electron positron scattering process represented by . ... Møller scattering is the name given to electron-electron scattering in Quantum Field Theory. ... In quantum electrodynamics, 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. ... (help· info), (from the German bremsen, to brake and Strahlung, radiation, thus, braking radiation), is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus. ... Positronium (Ps) is a quasi-stable system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom. The orbit of the two particles and the set of energy levels is similar to that of the hydrogen atom (electron and proton). ...

Maximum Abelian gauge

In any non-Abelian gauge theory, any maximum Abelian gauge is an incomplete gauge which fixes the gauge freedom outside of the maximum Abelian subgroup. Examples are Abelian, in mathematics, is used in many different definitions: In group theory: Abelian group, a group in which the binary operation is commutative Category of abelian groups Ab has abelian groups as objects and group homomorphisms as morphisms Metabelian group is a group where the commutator subgroup is contained in... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ...

• For SU(2) gauge theory in D dimensions, the maximum Abelian subgroup is a U(1) subgroup. If this is chosen to be the one generated by the Pauli matrix σ₃, then the maximum Abelian gauge is that which maximizes the function

 where 

• For SU(3) gauge theory in D dimensions, the maximum Abelian subgroup is a U(1)XU(1) subgroup. If this is chosen to be the one generated by the Gell-Mann matrices λ₃ and λ₈, then the maximum Abelian gauge is that which maximizes the function

 where 

In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... The Pauli matrices are a set of 2 × 2 complex Hermitian matrices developed by Pauli. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... The Gell-Mann matrices, named after Murray Gell-Mann, are the infinitesimal generators of su(3). ...

Less commonly used gauges

Weyl gauge

The Weyl gauge (also known as the Hamiltonian or temporal gauge) is an incomplete gauge obtained by the choice

φ = 0

It is named after Hermann Weyl. Hermann Klaus Hugo Weyl (November 9, 1885 – December 9, 1955) was a German mathematician. ...

Multipolar gauge

The gauge condition of the Multipolar gauge, Line gauge or Poincaré gauge is:

where is the position vector and is the vector potential. In vector calculus, a vector potential is a vector field whose curl is a given vector field. ...

Fock-Schwinger gauge

The gauge condition of the Fock-Schwinger gauge (sometimes called the relativistic Poincaré gauge) is:

x^μA_μ = 0

where x^μ is the position four-vector and A_μ is the four-potential. Electromagnetic potential is . ...

References and external links

• Landau and Lifschitz, "The classical theory of fields"
• Jackson, "Classical Electrodynamics"
• J. D. Jackson, http://arxiv.org/abs/physics/0204034