Anomalous properties of spin-extended chiral fermions

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.