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

TL;DR

This paper establishes an exact relation between canonical and metric energy-momentum tensors in higher derivative tensor field theories, extending previous results to more complex actions with higher derivatives.

Contribution

It introduces a modified Noether's procedure for curved spacetime to relate these tensors in higher derivative theories, revealing a more general difference form.

Findings

The difference between the tensors has a more general form for higher derivatives.

The integral of the difference over spacetime reduces to a surface integral at infinity.

The relation holds in flat spacetime with implications for conserved quantities.

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 the Noether's procedure for curved space-time. For considered case the difference between these two tensors turns out to have 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 integral over 2-dimensional surface that is infinitely remote in the spacelike directions.