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. https://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 | ||||||
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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 | ||||||
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Series Name: | Contemp. Math. | ||||||
Issue or Number: | 132 | ||||||
Record Number: | CaltechAUTHORS:20100810-093244959 | ||||||
Persistent URL: | https://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: | 03 Oct 2019 01:55 |
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