Covariantizing Classical Field Theories

TL;DR

This paper introduces a method to enlarge the covariance group of classical field theories, making them generally covariant and free of absolute objects, thus generalizing existing parametrization techniques.

Contribution

It presents a novel technique to covariantize classical field theories, extending Dirac and Kuchař's parametrization to internal covariance groups and deriving key concepts like minimal coupling.

Findings

Enlarged covariance groups make theories generally covariant.

Method applies to internal covariance groups, deriving minimal coupling.

The technique preserves the essential equivalence to original theories.

Abstract

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.