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Stress‐Tensor Commutators and Schwinger Terms

Boulware, David G. and Deser, S. (1967) Stress‐Tensor Commutators and Schwinger Terms. Journal of Mathematical Physics, 8 (7). pp. 1468-1477. ISSN 0022-2488.

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We investigate, in local field theory, general properties of commutators involving Poincaré generators or stress‐tensor components, particularly those of local commutators among the latter. The spectral representation of the vacuum stress commutator is given, and shown to require the existence of singular "Schwinger terms'' at equal times, similar to those present in current commutators. These terms are analyzed and related to the metric dependence of the stress tensor in the presence of a prescribed of a prescribed gravitational field and some general results concerning this dependence presented. The resolution of the Schwinger paradox for the T^(μν) commutators is discussed together with some of its implications, such as "nonclassical'' metric dependence of T^(μν). A further paradox concerning the vacuum self‐stress—whether the stress tensor or its vacuum‐subtracted value should enter in the commutators—is related to the covariance of the theory, and partially resolved within this framework.

Item Type:Article
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Deser, S.0000-0001-9285-9434
Additional Information:© 1967 The American Institute of Physics. (Received 2 December 1966) Supported in part by the U.S. Atomic Energy Commission and by U.S. Air Force, Office of Scientific Research Grant 368-65.
Funding AgencyGrant Number
Atomic Energy CommissionUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)AF 368-65
John Simon Guggenheim FoundationUNSPECIFIED
Issue or Number:7
Record Number:CaltechAUTHORS:20181120-133839887
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91088
Deposited By: George Porter
Deposited On:20 Nov 2018 22:01
Last Modified:03 Oct 2019 20:31

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