Eur. Phys. J. Plus (2019) 134: 21
https://doi.org/10.1140/epjp/i2019-12359-x

Regular Article

Exact relation between canonical and metric energy-momentum tensors for higher derivative tensor field theories

Saint Petersburg State University, Saint Petersburg, Russia

^* e-mail: pastonsergey@gmail.com

Received: 20 July 2018
Accepted: 3 November 2018
Published online: 14 January 2019

Abstract

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.