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.

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

References in corpus (5)

• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Lorentz Invariance in Chiral Kinetic Theory
• Topological spin transport of relativistic electron
• Bobbing and Kicks in Electromagnetism and Gravity
• Berry's phase and the anomalous velocity of Bloch wavepackets

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• Wigner-Souriau translations and Lorentz symmetry of chiral fermions
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• Semiclassical analysis of Dirac fields on curved spacetime
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Lorentz transformations, sideways shift and massless spinning particles
• Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals
• Berry phase in the phase space worldline representation: the axial anomaly and classical kinetic theory
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Anomalous Hall effects beyond Berry magnetic fields in a Weyl metal phase
• Quantum geometrical effects in non-Hermitian systems
• Conformal symmetry, chiral fermions and semiclassical approximation
• Quantum geometric tensors from sub-bundle geometry
• The precession of particle spin in spherical symmetric spacetimes
• World-line formulation of chiral kinetic theory in topological background gauge fields
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Geometric phase for Dirac Hamiltonian under gravitational fields in the non-relativistic regime
• Spin Hall effects and the localization of massless spinning particles
• Generalised Geometric Phase
• Anomalous Hall Effect for semiclassical chiral fermions