SOME OBSERVATIONS ON NONCOVARIANT GAUGES AND THE ε-TERM

Abstract

We consider the Lagrangian path-integrals in Minkowski space for gauges with a residual gauge-invariance. From rather elementary considerations, we demonstrate the necessity of inclusion of an ε-term (even) in the formal treatments, without which one may reach incorrect conclusions. We show, further, that the ε-term can contribute to the BRST WT-identities in a nontrivial way (even as ε → 0). We also show that the (expectation value of the) correct ε-term satisfies an algebraic condition. We show by considering (a commonly used) example of a simple local quadratic ε-term, that lead to additional constraints on Green's function that are not normally taken into account in the BRST formalism which ignores the ε-term, and that they are characteristic of the way the singularities in propagators are handled. We argue that for a subclass of these gauges, the Minkowski path-integral could not be obtained by a Wick rotation from a Euclidean path-integral.