Covariantizing Classical Field Theories

We show how to enlarge the covariance group of any classical field theory in such a way that the resulting "covariantized" theory is 'essentially equivalent' to the original. In particular, our technique will render any classical field theory generally covariant, that is, the covariantized theory will be spacetime diffeomorphism-covariant and free of absolute objects. Our results thus generalize the well-known parametrization technique of Dirac and Kucha\v{r}. Our constructions apply equally well to internal covariance groups, in which context they produce natural derivations of both the Utiyama minimal coupling and St\"uckelberg tricks.