Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles

Understand

We consider the relation between spin and the Berry-phase contribution to the anomalous velocity of massive and massless Dirac particles.

• We extend the Berry connection that depends only on the spatial components of the particle momentum to one that depends on the the space and time components in a covariant manner.
• We show that this covariant Berry connection captures the Thomas-precession part of the Bargmann-Michel-Telegdi spin evolution, and contrast it with the traditional (unitary, but not naturally covariant) Berry connection that describes spin-orbit coupling.
• We then consider how the covariant connection enters the classical relativistic dynamics of spinning particles due to Mathisson, Papapetrou and Dixon.