Covariantizing Classical Field Theories

Abstract

We show how to enlarge the covariance groups of a wide variety of classical field theories in such a way that the resulting “covariantized” theories are éssentially equivalent to the originals. In particular, our technique will render many classical field theories generally covariant, that is, the covariantized theories will be spacetime diffeomorphism-covariant and free of absolute objects. Our results thus generalize the well-known parametrization technique of Dirac and Kuchar. Our constructions apply equally well to internal covariance groups, in which context they produce natural derivations of both the Utiyama minimal coupling and Stückelberg tricks.