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

Abstract

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. We discuss the problems that arise with Lorentz covariance in the massless case, and trace them mathematically to a failure of the Wigner-translation part of the massless-particle little group to be an exact gauge symmetry in the presence of interactions, and physically to the fact that the measured position of a massless spinning particle is necessarily observer dependent.

arXiv comment38 pages, 0 figures, RevTex4. Revised version has added references, and some typos fixed

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• World-line construction of a covariant chiral kinetic theory
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• Chiral fermions as classical massless spinning particles
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• Wigner-Souriau translations and Lorentz symmetry of chiral fermions
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• Probing Wigner Rotations for Any Group
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• How does the photon's spin affect Gravitational Wave measurements?
• A Semiclassical Kinetic Theory of Dirac Particles and Thomas Precession
• Abelian and non-Abelian Berry curvatures in lattice QCD
• Quantum geometrical effects in non-Hermitian systems
• Conformal symmetry, chiral fermions and semiclassical approximation
• Pryce's mass-center operators and the anomalous velocity of a spinning electron
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• Quantum geometric tensors from sub-bundle geometry
• Geometric phase for Dirac Hamiltonian under gravitational fields in the non-relativistic regime
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• World-line formulation of chiral kinetic theory in topological background gauge fields
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Generalised Geometric Phase
• Spin Hall effects and the localization of massless spinning particles
• Anomalous Hall Effect for semiclassical chiral fermions