Imprints from a Riemann-Cartan space-time on the energy levels of Dirac spinors

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.

12 pages; v2: minor corrections and additions

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Cited by in corpus (9)

• Observational Constraints in Metric-Affine Gravity
• Induced gravitational topological term and the Einstein-Cartan modified theory
• Schrödinger equation in a general curved space-time geometry
• Signature of Einstein-Cartan theory
• Cartan $F(R)$ Gravity and Equivalent Scalar-Tensor Theory
• Nonassociative Einstein-Dirac-Maxwell systems and R-flux modified Reissner-Nordström black holes and wormholes
• Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions
• About the (in)equivalence between holonomic versus non-holonomic theories of gravity
• Robustness of predicted CMB fluctuations in Cartan $F(R)$ gravity