On the interaction of massive spinor particles with external electromagnetic and torsion fields

TL;DR

This paper investigates the Dirac equation with external electromagnetic and torsion fields, introducing a nonminimal interaction, analyzing symmetries, and deriving classical particle motion in a constant torsion background.

Contribution

It introduces a nonminimal coupling of spinor fields with torsion, revealing a symmetry between torsion and electromagnetic potentials, and performs a detailed Foldy-Wouthuysen transformation.

Findings

Identification of an extra local symmetry in the system

Derivation of the classical motion of particles in torsion fields

Extension of the Dirac equation to include nonminimal torsion interactions

Abstract

We explore the Dirac equation in external electromagnetic and torsion fields. Motivated by the previous study of quantum field theory in an external torsion field, we include a nonminimal interaction of the spinor field with torsion. As a consequence, the torsion axial vector and the electromagnetic potential enter the action in a similar form. The existence of an extra local symmetry is emphasized and the Foldy-Wouthuysen transformation is performed to an accuracy of next to the leading order. We also discuss the motion of a classical test particle in a constant torsion field.