The physical meaning of the Belinfante-Rosenfeld ambiguity

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. We argue this follows from Noether's second theorem and show that certain examples of BR ambiguities reduce to large gauge transformations.

7+2 pages; v2:version accepted for pubication in Physical Review D, 7+4 pages, modified abstract, extended discussion, added 1 figure, added 2 appendices with examples