A Quantum Field-Theoretical Perspective on Scale Anomalies in 1D systems with Three-Body Interactions

TL;DR

This paper investigates scale anomalies in one-dimensional quantum systems with three-body interactions, revealing their connection to two-dimensional systems and analyzing scattering properties through regularization methods.

Contribution

It provides a detailed quantum field-theoretical analysis of scale anomalies in 1D three-body systems, linking thermodynamic and energy-momentum tensor perspectives.

Findings

Identification of scale anomaly in 1D three-body systems

Analysis of scattering amplitudes and bound states

Connection between thermodynamic anomaly and energy-momentum tensor trace

Abstract

We analyze, from a canonical quantum field theory perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in two-dimensional systems with two-body interactions. We study in detail the properties of the scattering amplitude including both bound and scattering states, using cutoff and dimensional regularization, and clarify the connection between the scale anomaly derived from thermodynamics to the non-vanishing nonrelativistic trace of the energy-momentum tensor.