Chiral fermions as classical massless spinning particles

Understand

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.