Chiral fermions as classical massless spinning particles

TL;DR

This paper explores semiclassical models of chiral fermions with Berry curvature, revealing their symmetries, coupling to electromagnetic fields, and resulting unusual motions such as superluminal and spiraling trajectories.

Contribution

It connects Souriau's classical spinning particle model to chiral fermions, identifying Berry curvature with classical spin and analyzing symmetry breaking and unconventional motions.

Findings

Berry term corresponds to classical spin two-form

Spin enslavement breaks boost symmetry

Superluminal Hall-type motions observed for g=0

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 Poincar\'e 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.