Gauge fixing and physical symmetries

Abstract

We analyze how gauge fixing, which is required by any practical continuum approach to gauge systems, can interfere with the physical symmetries of such systems. In principle, the gauge fixing procedure, which deals with the (unphysical) gauge symmetry, should not interfere with the other (physical) symmetries. In practice, however, there can be an interference which takes two different forms. First, depending on the considered gauge, it might not always be simple or possible to devise approximation schemes that preserve the physical symmetry constraints on (gauge-independent) observables. Second, even at an exact level of discussion, the (gauge-dependent) effective action for the gauge field, and thus the related vertex functions, may not reflect the physical symmetries of the problem. We illustrate these difficulties using a very general class of gauge fixings that contains the usual gauge fixings as particular cases. Using background field techniques, we then propose specific gauge choices that allow one to keep the physical symmetries explicit, both at the level of the observables and at the level of the effective action for the gauge field. Our analysis is based on the notion of invariance modulo gauge transformations. This is not only a convenient framework to discuss symmetries in the presence of unphysical degrees of freedom, but it also allows one to reinterpret certain well known phenomena in gauge theories without the need to invoke the conceptually annoying ``breaking of a gauge symmetry''.