Gauge fixing

Gauge fixing imposes a condition that selects representatives from classes of mathematically equivalent field configurations. It removes redundant descriptions without changing gauge-invariant physical predictions.

Gauge symmetry: A symmetry relating different mathematical descriptions of the same physical state. Gauge fixing chooses one description from the equivalence generated by this symmetry.
Gauge theory: A field theory whose descriptions have local transformation redundancies. Gauge fixing is a procedure used within this broader class of theories.
Gauge-invariant formulation: A formulation that preserves gauge symmetry without selecting a particular representative. It avoids choosing a gauge, unlike conventional gauge-fixed calculations.
Covariant quantization: A quantization approach that preserves manifest spacetime covariance in its equations. Gauge fixing permits covariant calculations while managing unphysical field components.
Gauge orbit: The set of field configurations related by gauge transformations. A gauge condition selects representatives from these orbits.
Gauge transformation: A local transformation of fields that preserves gauge-invariant physical content. Such transformations generate the equivalent descriptions that fixing aims to distinguish.
Axial gauge: A gauge condition setting a field component along a chosen direction to zero. It offers a different choice from covariant conditions such as Lorenz gauge.
Quantum electrodynamics: The quantum field theory of electromagnetic interactions between charged particles and photons. Photon propagators are commonly calculated after choosing a gauge.
Lorenz gauge: The condition ∂μAμ = 0 imposed on the electromagnetic four-potential. It is a familiar differential gauge condition used to simplify electromagnetic equations.
Gauge-invariant observable: A physical quantity unchanged by gauge transformations. Gauge fixing must leave these observables independent of the chosen condition.

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