Exact relation between canonical and metric energy-momentum tensors for higher derivative tensor field theories
Saint Petersburg State University, Saint Petersburg, Russia
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Accepted: 3 November 2018
Published online: 14 January 2019
We discuss the relation between canonical and metric energy-momentum tensors for field theories with actions that can depend on the higher derivatives of tensor fields in a flat spacetime. In order to obtain it we use a modification of Noether's procedure for curved spacetime. For the considered case the difference between these two tensors turns out to have a more general form than for theories with no more than first-order derivatives. Despite this fact we prove that the difference between corresponding integrals of motion still has the form of an integral over 2-dimensional surface that is infinitely remote in the spacelike directions.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019