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| axial gauge | |
|---|---|
| Name | axial gauge |
| Type | gauge fixing condition |
| Field | Quantum field theory |
| Introduced | 1960s |
| Related | Faddeev–Popov procedure, BRST symmetry |
axial gauge
Axial gauge is a class of gauge-fixing choices in Quantum field theory defined by imposing a linear condition n·A=0 with a fixed nonzero four-vector n. It is used in studies of Quantum chromodynamics, Electroweak interaction calculations, and perturbative analyses in gauges such as the light-cone and temporal gauges. The axial prescription influences propagator structure, residual symmetries, and nonperturbative issues that connect to work by authors associated with the Faddeev–Popov procedure, Gribov problem, and BRST symmetry.
The axial condition sets n·A(x)=0 for a chosen constant vector n, where A is the gauge potential in theories like Yang–Mills theory and Quantum electrodynamics. In nonabelian contexts such as Quantum chromodynamics and models studied within Perturbation theory, this constraint removes many gauge degrees of freedom while preserving manifest locality along directions orthogonal to n. For specific choices of n, known special cases include the temporal gauge (n=(1,0,0,0)) used in canonical analyses by researchers connected to Dirac canonical quantization and the light-cone gauge (n lightlike) applied in work following Paul Dirac and later developments by groups linked to Bjorken and Kogut. The axial condition affects residual gauge transformations tied to global symmetries treated in contexts involving Noether's theorem studies and algebraic structures similar to those in analyses by authors from Institute for Advanced Study and major university groups working on gauge fixing.
Common variants include the temporal gauge, spatial axial gauges, and the light-cone gauge; each corresponds to choices of n such as time-like, space-like, or null directions used in computations at institutions like CERN and SLAC National Accelerator Laboratory. Implementations often supplement n·A=0 with prescriptions for singular denominators, for example principal-value or Mandelstam–Leibbrandt prescriptions developed by researchers associated with Mandelstam and Leibbrandt, and applied in calculations by teams at Harvard University and Princeton University. Alternatives mix axial constraints with partial covariant gauges in hybrid schemes examined in collaborations involving groups at Massachusetts Institute of Technology and Stanford University. These choices influence renormalization strategies employed in renormalization studies by authors connected to Gerard 't Hooft and Kenneth G. Wilson.
Canonical and path-integral quantizations of axial-type gauges produce propagators with characteristic n-dependent numerator structures; derivations trace through techniques used in the Faddeev–Popov procedure and have been refined by practitioners working at laboratories like CERN and universities such as Yale University. The axial propagator often contains spurious poles of the form 1/(k·n) requiring regularization, a problem addressed by the Mandelstam–Leibbrandt prescription and alternative treatments advanced in papers from groups linked to University of Cambridge and Columbia University. Perturbative loop calculations in Quantum chromodynamics using axial gauges require consistent pole prescriptions to maintain gauge invariance under transformations akin to those studied by Gerard 't Hooft and to preserve BRST-related identities explored by researchers at Institute for Advanced Study.
Even after imposing n·A=0, residual gauge transformations that satisfy n·Dω=0 can remain; analyses of these transformations connect to global issues examined in the Gribov problem, originally formulated by investigators at institutions including Landau Institute for Theoretical Physics. The presence of Gribov copies in nonabelian configurations influences confinement-related studies conducted in collaboration with teams from Landau Institute and IHEP and intersects with work on BRST symmetry anomalies by groups at Lebedev Physical Institute. Methods to restrict to regions free of copies, analogous to the Gribov horizon construction developed by Vladimir Gribov and others, have been adapted to axial settings in research programs at SISSA and University of Amsterdam.
Axial gauges are widely used in high-energy scattering computations in Quantum chromodynamics and in factorization proofs common to analyses undertaken at Brookhaven National Laboratory and CERN. The light-cone axial variant facilitates parton-model formulations related to work by Bjorken and applied in perturbative studies by collaborations at SLAC National Accelerator Laboratory and DESY. Axial choices simplify polarization sums in calculations tied to amplitudes studied at Perimeter Institute and to resummation techniques developed by groups at Rutgers University and University of Chicago. These gauges can reduce ghost contributions in loop diagrams, a feature exploited in computational approaches developed by teams associated with Fermilab.
On the lattice, implementing axial constraints requires discrete analogues of n·A=0 and has been studied by lattice groups at CERN and Brookhaven National Laboratory. Nonperturbative phenomena such as confinement and topology in Yang–Mills theory are sensitive to gauge-fixing ambiguities; investigations by collaborations from University of Glasgow and University of Pisa examine Gribov copy effects and gauge-fixing algorithms. Numerical approaches leveraging axial-like conditions have been pursued within projects affiliated with Argonne National Laboratory and European lattice consortia, often comparing outcomes with results in gauges used by research groups at University of Edinburgh and ETH Zurich.
Axial gauges relate to covariant gauges, Coulomb gauge, and light-front quantization through explicit gauge transformations studied in formal work by authors at Princeton University and Harvard University. Transitions between axial and covariant descriptions require attention to boundary conditions and to BRST cohomology structures examined by teams at Max Planck Institute for Physics and Institut des Hautes Études Scientifiques. Practical comparisons of computational efficiency and infrared behavior inform choices in phenomenology pursued by groups at CERN, SLAC National Accelerator Laboratory, and national laboratories such as KEK.