Path-Integral Derivation of the Non-relativistic Scale Anomaly

TL;DR

This paper derives the non-relativistic scale anomaly for a 2D Bose gas with contact interactions using a novel path-integral approach, providing a new perspective on quantum anomalies in many-body systems.

Contribution

It introduces a path-integral derivation of the scale anomaly in non-relativistic quantum gases, expanding the toolkit for analyzing quantum anomalies in these systems.

Findings

Path-integral method successfully reproduces known anomaly values.

Natural regulators identified that yield correct anomaly calculations.

Applicable to both vacuum and many-body quantum systems.

Abstract

In this paper we calculate the scale anomaly for a quantum field theoretic 2D-nonrelativistic Bose gas with contact interactions using Fujikawa's method, both in vacuum and in many-body systems. The use of path integrals for these problems is novel and motivated by a recently developed path-integral framework for addressing questions about scaling in these systems. A natural class of regulators is found that produces the correct value of the anomaly traditionally calculated via other methods, e.g., diagrammatically via the beta function.