Belinfante type invariance of the Noether identities in a riemannian and a Weitzenböck spacetime

Abstract

The energy-momentum and angular momentum Noether identities for a matter field in the Minkowski spacetime of special relativity are invariant under a relocalization of their canonical currents by means of superpotentials. We extend this invariance for the angular momentum identity to the Riemann-Cartan spacetime of the Poincaré gauge theory of gravity (PGT). For the energy-momentum identity we find sufficient conditions which guarantee appropriate relocalization in a Riemannian and in a Weitzenböck spacetime. In particular, we recover the symmetric, divergence-free Belinfante-Rosenfeld energy-momentum current of general relativity.