gaugefixed

Gauge-fixed is a term used in gauge theories to describe a formulation in which a gauge condition has been imposed to remove redundant degrees of freedom. Because gauge invariance allows multiple mathematical potentials to describe the same physical field, fixing a gauge selects one representative from each gauge orbit. This makes quantization, perturbation theory, and certain calculations well defined by eliminating unphysical variations.

Common gauge choices include Lorenz gauge, where the condition ∂μA^μ = 0 is imposed; Coulomb gauge, ∇·A = 0; and temporal gauge, A0 = 0. In covariant gauges, a gauge-fixing term is added to the Lagrangian, such as (1/2ξ)(∂μA^μ)^2, introducing a gauge parameter ξ. For non-Abelian theories, gauge fixing in the path integral also introduces the Faddeev-Popov determinant and, correspondingly, ghost fields, which ensure the correct counting of physical degrees of freedom in quantum calculations.

Residual gauge freedom and Gribov ambiguities can arise: in some gauges there remain gauge transformations that preserve the gauge condition, and in non-Abelian theories there can be multiple gauge-equivalent configurations (Gribov copies) satisfying the same condition. These issues affect nonperturbative formulations and require careful treatment.

In practice, gauge fixing is essential for defining propagators and performing calculations, though physical observables are gauge-invariant. Gauge-fixed formulations are used across quantum electrodynamics and quantum chromodynamics, while lattice gauge theory often treats gauge fixing as optional for many observables. The term denotes the standard state after imposing a gauge condition, with the specific gauge choice influencing intermediate steps but not the final physical results.