# American Institute of Mathematical Sciences

December  2011, 3(4): 487-506. doi: 10.3934/jgm.2011.3.487

## Covariantizing classical field theories

 1 ICMAT (CSIC, UAM, UC3M, UCM), Departamento de Geometría y Topología, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain 2 Paciﬁc Institute for the Mathematical Sciences, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

Received  August 2010 Revised  January 2011 Published  February 2012

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 `essentially 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 Kuchař. 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.
Citation: Marco Castrillón López, Mark J. Gotay. Covariantizing classical field theories. Journal of Geometric Mechanics, 2011, 3 (4) : 487-506. doi: 10.3934/jgm.2011.3.487
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