Spin dynamics with non-abelian Berry gauge fields as a semiclassical constrained hamiltonian system

TL;DR

This paper develops a semiclassical framework for spin dynamics influenced by non-abelian Berry gauge fields, using constrained Hamiltonian systems to analyze phenomena like Thomas precession and the spin Hall effect.

Contribution

It introduces a systematic semiclassical approach to spin dynamics with non-abelian Berry gauge fields, clarifying complex phenomena and providing new formulations for effects like the spin Hall effect.

Findings

Calculated the force on an electron due to Berry gauge fields.

Clarified the role of Berry gauge fields in Thomas precession.

Presented a semiclassical formulation of the spin Hall effect.

Abstract

The dynamics of observables which are matrices depending on \hbar and taking values in classical phase space is defined retaining the terms up to the first order in \hbar of the Moyal bracket. Within this semiclassical approach a first order lagrangian involving gauge fields is studied as a constrained hamiltonian system. This provides a systematic study of spin dynamics in the presence of non-abelian Berry gauge fields. We applied the method to various types of dynamical spin systems and clarified some persisting discussions. In particular employing the Berry gauge field which generates the Thomas precession, we calculated the force exerted on an electron in the external electric and magnetic fields. Moreover, a simple semiclassical formulation of the spin Hall effect is accomplished.