The physical meaning of the Belinfante-Rosenfeld ambiguity

TL;DR

This paper clarifies the physical meaning of the Belinfante-Rosenfeld ambiguity in energy-momentum and spin tensors, especially in Einstein-Cartan spacetimes, by interpreting it as a choice in splitting conserved currents.

Contribution

It provides a new physical interpretation of the Belinfante-Rosenfeld ambiguity using bi-form formalism applicable to conserved currents and gauge fields.

Findings

Reinterprets the BR ambiguity as a splitting choice in conserved currents.

Applies bi-form formalism to Einstein-Cartan spacetimes.

Offers a physical understanding of spin polarization and its transport.

Abstract

Current literature lacks consensus on how to theoretically describe spin polarization and its transport in matter. The underlying reason is the presence of the Belinfante-Rosenfeld (BR) ambiguity in the form of the energy-momentum and spin tensors. I re-examine the BR ambiguity in Einstein-Cartan spacetimes, using the bi-form formalism in a manner applicable to any conserved current and its corresponding gauge field. This allows us to physically interpret the BR ambiguity as the choice of splitting a conserved current into its matter and gauge field contributions.