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  • Letter
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  • Access by Xinjiang University

Physical meaning of the Belinfante-Rosenfeld ambiguity

Ioannis Matthaiakakis*

  • *Contact author: i.matthaiakakis@soton.ac.uk
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Phys. Rev. D 114, L081703 – Published 29 October, 2026

DOI: https://doi.org/10.1103/9ztc-9pmf

Abstract

The 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 biform 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. I argue this follows from Noether’s second theorem and show that certain examples of BR ambiguities reduce to large gauge transformations.

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Phys. Rev. D 114, L081703– Published 29 October, 2026
  • Received 5 April 2026
  • Accepted 25 September 2026
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