Topological spin transport of relativistic electron

Abstract

We derive the semiclassical (with accuracy of $\hslash$) motion equation for relativistic electron, which follow from the Dirac equation. We determine both the evolution equation for electron polarization, which takes the non-Abelian Berry phase into account, and Hamiltonian equations for trajectories of the particle (wave packet) center in the phase space. The equations have covariant form with respect to U(2) gauge transformations and contain topological spin terms that are connected to the Berry gauge field arising during the diagonalization of the Dirac equation. The trajectory equations obtained are substantially different from the traditional ones (for instance, those that follow from the Pauli Hamiltonian) and correspond to contemporary ideas of topological spin transport of particles.

10 pages, to appear in Europhysics Letters

References in corpus (3)

• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• Topological spin transport of photons: "magnetic monopole" gauge field in Maxwell equations and polarization splitting of rays in periodically inhomogeneous media

Cited by in corpus (1)

• On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature