Gaugechange

Gaugechange refers to the freedom to alter the mathematical description of fields in gauge theories without changing physical predictions. In these theories, certain field configurations are related by gauge transformations, which operate as a local symmetry. The transformations reflect redundant degrees of freedom in the field variables rather than new physical content.

A familiar example is electromagnetism, where the four-potential Aμ can be transformed as Aμ → Aμ + ∂μ Λ(x) without changing the electric and magnetic fields. The field strength tensor Fμν = ∂μ Aν − ∂ν Aμ remains invariant under this change, so observable quantities do not depend on the specific choice of gauge. Similar gauge freedoms occur in non-Abelian gauge theories, where the potentials take values in a Lie algebra and transform as Aμ → U Aμ U⁻¹ + (i/g)(∂μ U)U⁻¹, with U(x) a local gauge matrix. Here, the action and physical observables are gauge invariant, even though the potentials themselves change.

Gaugefixing is the process of selecting a particular representative from each gauge equivalence class to simplify calculations, using conditions such as the Lorenz gauge ∂μ Aμ = 0 or the Coulomb gauge ∇·A = 0. In quantum field theory, gaugefixing is accompanied by procedures like Faddeev–Popov quantization and, in some formulations, BRST symmetry to maintain consistency.

In practice, gaugechange emphasizes that only gauge-invariant quantities have direct physical meaning, while different gauge choices provide convenient mathematical descriptions of the same underlying physics. See also gauge theory, gauge invariance, and gauge fixing.