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We consider the relation between spin and the Berry-phase contribution to theanomalous velocity of massive and massless Dirac particles. We extend the Berryconnection that depends only on the spatial components of the particle momentumto one that depends on the the space and time components in a covariant manner.We show that this covariant Berry connection captures the Thomas-precessionpart of the Bargmann-Michel-Telegdi spin evolution, and contrast it with thetraditional (unitary, but not naturally covariant) Berry connection thatdescribes spin-orbit coupling. We then consider how the covariant connectionenters the classical relativistic dynamics of spinning particles due toMathisson, Papapetrou and Dixon. We discuss the problems that arise withLorentz covariance in the massless case, and trace them mathematically to afailure of the Wigner-translation part of the massless-particle little group tobe an exact gauge symmetry in the presence of interactions, and physically tothe fact that the measured position of a massless spinning particle isnecessarily observer dependent.

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