The physical meaning of the Belinfante-Rosenfeld ambiguity
Ioannis Matthaiakakis
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.