https://doi.org/10.1140/epjc/s10052-023-11812-4
Regular Article - Theoretical Physics
Sources of torsion in Poincarè gauge gravity
Department of Physics, Utah State University, Logan, Utah, USA
Received:
27
April
2023
Accepted:
8
July
2023
Published online:
26
July
2023
We study sources for torsion in Poincarè gauge theory in any dimension, signature, and spin. We find that symmetric kinetic terms for non-Yang–Mills bosonic fields of arbitrary rank drive torsion. Our detailed discussion of spin-3/2 Rarita–Schwinger fields shows that they source all independent parts of the torsion. We develop systematic notation for spin-(2k+1)/2 fields and find the spin tensor for arbitrary k in n 
2k+1 dimensions. For 
there is a novel direct coupling between torsion and spinor fields. We also cast the well-known gauge relation between the canonical and Belinfante–Rosenfield energy tensors in terms of different choices of independent variables.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
