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

TL;DR

This paper studies how torsion in Riemann-Cartan spacetime affects fermion energy levels, revealing Zeeman-like splitting and exploring potential detection methods in astrophysics, cosmology, and solid state physics.

Contribution

It introduces a model-independent analysis of torsion-fermion interactions, including non-minimal and parity-breaking couplings, and predicts observable energy level splittings.

Findings

Torsion causes Zeeman-like energy splitting in fermions and anti-fermions.

Energy level shifts depend on torsion alignment and specific couplings.

Potential detection of torsion effects in astrophysical and condensed matter systems.

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.