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Parametrization and stress–energy–momentum tensors in metric field theories

Castrillón López, Marco and Gotay, Mark J. and Marsden, Jerrold E. (2008) Parametrization and stress–energy–momentum tensors in metric field theories. Journal of Physics A: Mathematical and Theoretical, 41 (34). p. 344002. ISSN 1751-8113. http://resolver.caltech.edu/CaltechAUTHORS:CASjpa08

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Abstract

We give an exposition of the 1972 parametrization method of Kuchař in the context of the multisymplectic approach to field theory. The purpose of the formalism developed here is to make any classical field theory, containing a metric as a sole background field, generally covariant (that is, parametrized, with the spacetime diffeomorphism group as a symmetry group) as well as fully dynamic. This is accomplished by introducing certain 'covariance fields' as genuine dynamic fields. As we shall see, the multimomenta conjugate to these new fields form the Piola–Kirchhoff version of the stress–energy–momentum tensor field, and their Euler–Lagrange equations are vacuously satisfied. Thus, these fields have no additional physical content; they serve only to provide an efficient means of parametrizing the theory. Our results are illustrated with two examples, namely an electromagnetic field and a Klein–Gordon vector field, both on a background spacetime.


Item Type:Article
Related URLs:
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http://dx.doi.org/10.1088/1751-8113/41/34/344002DOIUNSPECIFIED
http://stacks.iop.org/JPhysA/41/344002PublisherUNSPECIFIED
Additional Information:Copyright © Institute of Physics and IOP Publishing Limited 2008. Received 13 December 2007. Published 11 August 2008. Print publication: Issue 34 (29 August 2008). We dedicate this paper to Darryl Holm on his 60th birthday. We thank him for his interest in the ideas in this paper and for his many inspiring works over the years. MJG and JEM thank the National Science Foundation for its occasional support of work of this sort. MCL was partially supported by DGSIC (Spain) under grant MTM2007-60017.
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National Science FoundationUNSPECIFIED
Spanish Ministry of Science and Technology (DGSIC)MTM2007-60017
Record Number:CaltechAUTHORS:CASjpa08
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Deposited On:15 Aug 2008 21:48
Last Modified:26 Dec 2012 10:14

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