Chiral fermions as classical massless spinning particles

Abstract

Semiclassical chiral fermion models with Berry term are studied in a symplectic framework. In the free case, the system can be obtained from Souriau's model for a relativistic massless spinning particle by "enslaving" the spin. The Berry term is identified with the classical spin two-form of the latter model. The Souriau model carries a natural Poincaré symmetry that we highlight, but spin enslavement breaks the boost symmetry. However the relation between the models allows us to derive a Poincare symmetry of unconventional form for chiral fermions. Then we couple our system to an external electromagnetic field. For gyromagnetic ratio $g=0$ we get curious superluminal Hall-type motions; for $g=2$ and in a pure constant magnetic field in particular, we find instead spiraling motions.

Substantially revised and extended version. 31 pages, 5 figures. Details clarified and references added. To be published in PRD

References in corpus (8)

• The Chiral Magnetic Effect
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Lorentz Invariance in Chiral Kinetic Theory
• Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
• Chiral Magnetic Spiral
• Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles
• Relativistic Particle and Relativistic Fluids: Magnetic Moment and Spin-Orbit Interactions
• Wong's Equations and Charged Relativistic Particles in Non-Commutative Space

Cited by in corpus (13)

• General treatment of quantum and classical spinning particles in external fields
• Constructing phase space distributions with internal symmetries
• Wigner translations and the observer-dependence of the position of masslesss spinning particles
• Wigner-Souriau translations and Lorentz symmetry of chiral fermions
• Relativistic Particle and Relativistic Fluids: Magnetic Moment and Spin-Orbit Interactions
• Lorentz transformations, sideways shift and massless spinning particles
• Topology of Generalized Spinors and Chiral Anomaly
• World sheets of spinning particles
• Two-twistor particle models and free massive higher spin fields
• Conformal symmetry, chiral fermions and semiclassical approximation
• Spin Hall effects and the localization of massless spinning particles
• Anomalous Hall Effect for semiclassical chiral fermions
• Geometric studies of the interplay between spin and gravity