Berry phase for spins of relativistic electrons

TL;DR

This paper explores the Berry phase in the context of relativistic electrons' spin states, revealing that its expression in spin space mirrors that in momentum space, thus extending the concept's applicability.

Contribution

It demonstrates that the Berry phase for electron spins in relativistic quantum mechanics has a consistent form across different parameter spaces, linking spin and momentum space descriptions.

Findings

Berry phase in spin space matches that in momentum space.

Provides a unified expression for Berry phase across different solution families.

Extends Berry phase concepts to relativistic electron spin solutions.

Abstract

Berry phase is a very general concept. It is applied here to families of solutions of the Dirac equation with different values of spin. The value of the Berry phase in the spin space is given by the same expression as was found before in the momentum space.