Classical anomalies for spinning particles

Abstract

We discuss the phenomenon of classical anomaly. It is observed for 3D Berezin-Marinov (BM), Barducci-Casalbuoni-Lusanna (BCL) and Cortes-Plyushchay-Velazquez (CPV) pseudoclassical spin particle models. We show that quantum mechanically these different models correspond to the same P,T-invariant system of planar fermions, but the quantum system has global symmetries being not reproducible classically in full in any of the models. We demonstrate that the specific U(1) gauge symmetry characterized by the opposite coupling constants of spin s=+1/2 and s=-1/2 states has a natural classical analog in CPV model but can be reproduced in BM and BCL models in an obscure and rather artificial form. We also show that BM and BCL models quantum mechanically are equivalent in any odd-dimensional space-time, but describe different quantum systems in even space-time dimensions.