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Stress-Energy-Momentum Tensors and the Belinfante-Rosenfeld Formula

Gotay, Mark J. and Marsden, Jerrold E. (1992) Stress-Energy-Momentum Tensors and the Belinfante-Rosenfeld Formula. In: Mathematical aspects of classical field theory. Contemp. Math. . No.132. American Mathematical Society , pp. 367-392. http://resolver.caltech.edu/CaltechAUTHORS:20100810-093244959

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Abstract

We present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory. The stress-energy-momentum tensor T ^μ _ν that we construct is defined using the (multi)momentum map associated to the spacetime diffeomorphism group. The tensor T ^μ _ν is uniquely determined as well as gauge-covariant, and depends only upon the divergence equivalence class of the Lagrangian. It satisfies a generalized version of the classical Belinfante-Rosenfeld formula, and hence naturally incorporates both the canonical stress-energy-momentum tensor and the “correction terms” that are necessary to make the latter well behaved. Furthermore, in the presence of a metric on spacetime, our T^(μν) coincides with the Hilbert tensor and hence is automatically symmetric.


Item Type:Book Section
Additional Information:© 1992. We are grateful for helpful discussions with Arthur Fischer, Hans Künzle, John Pierce, and Abe Taub. Research partially supported by NSF Grant DMS 88-05699. Research partially supported by NSF Grant DMS 89-22704
Funders:
Funding AgencyGrant Number
NSFDMS 88-05699
NSFDMS 89-22704
Record Number:CaltechAUTHORS:20100810-093244959
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100810-093244959
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19366
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:10 Aug 2010 21:27
Last Modified:26 Dec 2012 12:18

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