Berry phase for spin--1/2 particles moving in a spacetime with torsion

TL;DR

This paper investigates the Berry phase for spin-1/2 particles in a spacetime with torsion, revealing conditions under which a non-zero Berry phase occurs, especially for massless fermions perpendicular to background polarization.

Contribution

It demonstrates that a Berry phase arises only for massless fermions with specific momentum orientation in a torsioned spacetime with polarized background.

Findings

Berry phase exists only for massless fermions.

Berry phase depends on the orientation of momentum relative to polarization.

Order of magnitude discussed in various theoretical frameworks.

Abstract

Berry phase for a spin--1/2 particle moving in a flat spacetime with torsion is investigated in the context of the Einstein-Cartan-Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks.