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

Understand

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.