Parametrization and Stress-Energy-Momentum Tensors in Metric Field Theories

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dc.creatorLopez, Marco Castrillon
dc.creatorGotay, Mark J.
dc.creatorMarsden, Jerrold E.
dc.date2007-12-12
dc.date.accessioned2026-07-07T11:54:38Z
dc.date.available2026-07-07T11:54:38Z
dc.descriptionWe give an exposition of the parametrization method of Kuchar [1973] in the context of the multisymplectic approach to field theory, as presented in Gotay and Marsden [2008a]. The purpose of the formalism developed herein 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.
dc.description13 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0712.1883
dc.identifierhttp://arxiv.org/abs/0712.1883
dc.identifierJ.Phys.A41:344002,2008
dc.identifierdoi:10.1088/1751-8113/41/34/344002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/204970
dc.subjectMathematical Physics
dc.subject70S05; 70G75
dc.titleParametrization and Stress-Energy-Momentum Tensors in Metric Field Theories
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