Classical anomalies for spinning particles

TL;DR

This paper explores classical anomalies in various pseudoclassical spinning particle models, revealing how quantum symmetries differ from classical analogs and establishing model equivalences across dimensions.

Contribution

It demonstrates the existence of classical anomalies in multiple spin particle models and clarifies their quantum symmetry relations and dimensional equivalences.

Findings

Quantum models correspond to the same planar fermion system.

Classical models exhibit anomalies not present quantum mechanically.

BM and BCL models are equivalent in odd dimensions but differ in even dimensions.

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.