Chiral fermions as classical massless spinning particles
arXiv:1406.0718 · doi:10.1103/PhysRevD.91.045013
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 we get curious superluminal Hall-type motions; for and in a pure constant magnetic field in particular, we find instead spiraling motions.
arXiv commentSubstantially revised and extended version. 31 pages, 5 figures. Details clarified and references added. To be published in PRD
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