Anomalous properties of spin-extended chiral fermions

TL;DR

This paper investigates the properties of spin-extended chiral fermions, revealing differences from traditional models when coupled to electromagnetic fields and highlighting conditions under which Poincaré symmetry remains intact.

Contribution

It demonstrates the inequivalence of the spin-extended model to the chiral model under electromagnetic coupling and explores the conditions preserving Poincaré symmetry.

Findings

Spin-extended and chiral models are equivalent in free case but differ when coupled to electromagnetic fields.

The spin-extended model shows similar anomalous properties to the chiral model.

Poincaré symmetry remains unbroken when electric and magnetic fields are orthogonal.

Abstract

The spin-extended semiclassical chiral fermion (we call the S-model), which had been used to derive the twisted Lorentz symmetry of the "spin-enslaved" chiral fermion (we call the c-model) is equivalent to the latter in the free case, however coupling to an external electromagnetic field yields nonequivalent systems. The difference is highlighted by the inconsistency of spin enslavement within the spin-extended framework. The S-model exhibits nevertheless similar though slightly different anomalous properties as the usual c-model does. The natural Poincar\'e symmetry of the free model remains unbroken if the Pfaffian invariant vanishes, i.e., when the electric and magnetic fields are orthogonal, ${\bf E}\cdot{\bf B}=0$, as in the Hall effect.