Publication: Imprints from a Riemann-Cartan space-time on the energy levels of Dirac spinors
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2021-10-07
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IOP Publishing Ltd
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Abstract
In this work, we investigate the effects of the torsion-fermionic interaction on the energy levels of fermions within a Riemann-Cartan geometry using a model-independent approach. We consider the case of fermions minimally coupled to the background torsion as well as non-minimal extensions via additional couplings with the vector and axial fermionic currents which include parity-breaking interactions. In the limit of zero-curvature, and for the cases of constant and spherically symmetric torsion, we find a Zeeman-like effect on the energy levels of fermions and anti-fermions depending on whether they are aligned/anti-aligned with respect to the axial vector part of the torsion (or to specific combination of torsion quantities), and determine the corresponding fine-structure energy transitions. We also discuss non-minimal couplings between fermionic fields and torsion within the Einstein-Cartan theory and its extension to include the (parity-breaking) Holst term. Finally we elaborate on the detection of torsion effects related to the splitting of energy levels in astrophysics, cosmology and solid state physics using current capabilities.
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© 2021 IOP Publishing Ltd
We thank A Delhom for useful comments and insights. FC is funded by the FundacAo para a Ciencia e a Tecnologia (FCT, Portugal) doctoral Grant No. PD/BD/128017/2016. FSNL acknowledges support from the FCT Scientific Employment Stimulus contract with reference CEECIND/04057/2017. DRG is funded by the Atraccion de Talento Investigador program of the Comunidad de Madrid (Spain) No. 2018-T1/TIC-10431, and acknowledges further support from the Ministerio de Ciencia, Innovacion y Universidades (Spain) Project No. PID2019-108485GB-I00/AEI/10.13039/501100011033, the Spanish Project No. FIS2017-84440-C2-1-P (MINECO/FEDER, EU), the Project PROMETEO/2020/079 (Generalitat Valenciana), and the Edital 006/2018 PRONEX (FAPESQ-PB/CNPQ, Brazil) Grant No. 0015/2019. The authors also acknowledge funding from FCT Projects Nos. UID/FIS/04434/2020, CERN/FIS-PAR/0037/2019 andPTDC/FIS-OUT/29048/2017. FC thanks the hospitality of the Department of Theoretical Physics and IPARCOS of the Complutense University of Madrid, where part of this work was carried out. This article is based upon work from COST Action CA18108, supported by COST (European Cooperation in Science and Technology).