A Caltech Library Service

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.

PDF - Updated Version
See Usage Policy.


Use this Persistent URL to link to this item:


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
Funding AgencyGrant Number
NSFDMS 88-05699
NSFDMS 89-22704
Series Name:Contemp. Math.
Issue or Number:132
Record Number:CaltechAUTHORS:20100810-093244959
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19366
Deposited By: Ruth Sustaita
Deposited On:10 Aug 2010 21:27
Last Modified:03 Oct 2019 01:55

Repository Staff Only: item control page