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On the energy–momentum tensor

Ricardo E Gamboa Saraví

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We clarify the relation among canonical, metric and Belinfante's energy–momentum tensors for general tensor field theories. For any tensor field T, we define a new tensor field \widetilde {\bm T} in terms of which metric and Belinfante's energy–momentum tensors are readily computed. We show that the latter is the one that arises naturally from Noether's theorem for an arbitrary spacetime and it coincides on-shell with the metric one.


PACS

02.10.Ud Linear algebra

11.15.Ex Spontaneous breaking of gauge symmetries

MSC

83C75 Space-time singularities, cosmic censorship, etc.

81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)

15A69 Multilinear algebra, tensor products

Subjects

Mathematical physics

Particle physics and field theory

Dates

Issue 40 (8 October 2004)

Received 12 April 2004, in final form 10 August 2004

Published 22 September 2004



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