A note on quantum Hamiltonian reduction and anomalies

TL;DR

This paper presents a finite-dimensional Hamiltonian system with gauge symmetries that exhibits quantum anomalies due to the topology of the reduced phase space, challenging the notion that anomalies only arise from infinite degrees of freedom.

Contribution

It provides an explicit finite-dimensional example demonstrating that anomalies can originate from phase space topology, not just infinite degrees of freedom.

Findings

Finite-dimensional model with gauge symmetries shows anomalies

Anomalies linked to nontrivial topology of reduced phase space

Challenges the belief that anomalies require infinite degrees of freedom

Abstract

Quantization of field-theoretic models with gauge symmetries is often obstructed by quantum anomalies. It is commonly believed that the origin of these anomalies lies in the infinite number of degrees of freedom, which requires completing the model within an appropriate regularization scheme. This paper provides an explicit example of a finite-dimensional Hamiltonian system with first-class constraints whose quantization exhibits anomalies. These anomalies arise from the nontrivial topology of the reduced phase space.