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

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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). pp. 1-11. ISSN 1751-8113

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Official URL: http://iopscience.iop.org/1751-8121/41/34/344002/pdf/1751-8121_41_34_344002.pdf


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Abstract

We give an exposition of the 1972 parametrization method of Kuchar 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
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:21985
Deposited On:19 Jun 2013 15:52
Last Modified:12 Dec 2018 15:13

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