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  • Letter
  • Open Access

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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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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