puregauge

Puregauge is a term used in gauge theory to describe a configuration of a gauge field that is gauge-equivalent to the vacuum. A pure gauge configuration has vanishing field strength, F_mu nu = ∂_mu A_nu - ∂_nu A_mu + [A_mu, A_nu] = 0, and locally can be interpreted as a gauge artifact without physical electric or magnetic fields.

In a theory with gauge group G, a pure gauge potential can be written in the form A_mu(x) = (i/g) U(x) ∂_mu U(x)^{-1}, where U(x) is a smooth map from spacetime to G. This expression shows how the potential arises purely from a gauge transformation, leaving no local field strengths.

Global considerations add subtlety: even when F_mu nu vanishes, the configuration may reflect nontrivial topology or boundary conditions. The gauge function U(x) can possess nontrivial winding, and holonomy around non-contractible loops or nontrivial gauge bundles can carry topological information. Consequently, pure gauge configurations can be globally nontrivial in spaces with interesting topology or boundary conditions, yielding physical effects through quantities such as Wilson loops.

Puregauge concepts are important in practical contexts, including gauge fixing, the separation of physical and gauge degrees of freedom, and discussions of residual gauge freedom and Gribov ambiguities. On the lattice, a configuration is considered pure gauge if the link variables can be expressed as U_x,mu = g_x g_{x+mu}† for some site-dependent g_x.

See also: gauge theory, gauge transformation, field strength, Wilson loop, Gribov ambiguity.