Quantum Anomaly and Effective Field Description of a Quantum Chaotic Billiard

TL;DR

This paper explores the effective field theory of quantum chaotic billiards through quantum anomalies, revealing how anomalies affect operator commutators and enabling the introduction of phase variables without coarse-graining.

Contribution

It introduces a novel perspective on quantum anomalies in chaotic billiards, linking anomalies to effective dual fields and spectral functions without ensemble averaging.

Findings

Commutators of composite operators acquire anomalous parts.

Effective dual fields can be introduced without coarse-graining.

Spectral Husimi function acts as an amplitude in this framework.

Abstract

We investigate the effective field theory of a quantum chaotic billiard from a new perspective of quantum anomalies, which result from the absence of continuous spectral symmetry in quantized systems. It is shown that commutators of composite operators on the energy shell acquire anomalous part. The presence of the anomaly allows one to introduce effective dual fields as phase variables without any additional coarse-graining nor ensemble averaging in a ballistic system. The spectral Husimi function plays a role as the corresponding amplitude.