Procedure of coping with redundant degrees of freedom in physical field theories
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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 certain 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.
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.[citation needed]
In the physics of gauge theories, gaugefixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom...
In electromagnetism, the Lorenz gauge condition or Lorenz gauge (after Ludvig Lorenz) is a partial gaugefixing of the electromagnetic vector potential...
gauge Electroweak theory Gauge covariant derivative GaugefixingGauge gravitation theory Gauge group (mathematics) Kaluza–Klein theory Lorenz gauge Quantum...
catheters Gauge theory Gauge integral GaugefixingGauge boson Gauge (Minkowski functional) Gauge (knitting), the number of stitches in a given length Gauge (actress)...
rules by fixing the gauge. The traditional gaugefixing prescriptions of continuum electrodynamics select a unique representative from each gauge-transformation-related...
In gauge theory, especially in non-abelian gauge theories, global problems at gaugefixing are often encountered. Gaugefixing means choosing a representative...
potentials V and A is given in the article Gaugefixing, along with the precise statement of the nature of the gauge transformation. The relevant point here...
is, gaugefixing does not always fully fix the entire gauge symmetry, leaving behind some unfixed residual symmetry whose action leaves the gauge fixed...
}}{k^{2}}}}{k^{2}}}.} To find the Feynman rules for non-Abelian gauge fields, the procedure that performs the gaugefixing must be carefully corrected to account for a change...
\partial _{\mu }B^{\mu }=0\!} which may be called a generalized Lorenz gauge condition. For non-zero sources, with all fundamental constants included...
e. if the gaugefixing equations define a slice to the gauge action). The gauge-fixed potentials still have a gauge freedom under all gauge transformations...
transformations. Gauge theory Gauge covariant derivative GaugefixingGauge gravitation theory Kaluza–Klein theory Lie algebra Lie group Lorenz gauge Quantum chromodynamics...
unitarity gauge or unitary gauge is a particular choice of a gaugefixing in a gauge theory with a spontaneous symmetry breaking. In this gauge, the scalar...
Wess–Zumino gauge (a prescription for supersymmetric gaugefixing) provides a successful solution to this problem. Once such suitable gauge is obtained...
pseudo-Hermitian operators. The theory began with the application of BRST gaugefixing procedure to Langevin SDEs, that was later adapted to classical mechanics...
sacrifice manifest gauge symmetry by requiring gaugefixing. It's only after renormalization that gauge invariance can be recovered. Lattice field theory...
properties are not influenced by the specific choice of gauge. From the possible solutions for A, a gaugefixing introduced by Lev Landau is often used for charged...
mathematically elegant, with manifest gauge symmetry, for perturbative calculations it is necessary to fix a gauge. The gauge-fixing procedure was developed by Faddeev...
same system would correspond to a numerically different solution.) A "gaugefixing" is needed, i.e. we need to impose 4 (arbitrary) constraints on the coordinate...
of independent equations from 10 to 6, leaving the metric with four gauge-fixing degrees of freedom, which correspond to the freedom to choose a coordinate...
interpretation, and view the argument as a confusion about gauge invariance and gaugefixing instead.[citation needed] In a usual field equation, knowing...
potential A, and the electric scalar potential φ, are defined using gaugefixing such that: B = ∇ × A , E = − ∇ φ − ∂ A ∂ t . {\displaystyle {\begin{aligned}\mathbf...