FIELD STRENGTH-POTENTIAL CONNECTION IN NON-ABELIAN GAUGE THEORY

Given a non-Abelian field of the form f{hook}μν = f{hook}(x) f{hook}μν(x) we have found all possible potentials that generate a given field strength. We established the classes of non-gauge-equivalent potentials among them. These can be parametrized by the formula: Aμ = B0(X0(x), X1(x)) ∂μX0 + B1(X0(x), X1(x)) ∂μX1, where the functions B, X are defined in the text. We solved the same problem for general non-Abelian gauge fields in 2-dimensions. It turns out that the classes of non-gauge equivalent potentials are in close correspondence for the two problems. © 1979.