Path-Integral Derivation of the Non-relativistic Scale Anomaly

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.

arXiv comment8 pages (this version is the published version)

References in corpus (12)

• Bose-Einstein condensation in quasi2D trapped gases
• Observation of a pairing pseudogap in a two-dimensional Fermi gas
• Scale invariance and viscosity of a two-dimensional Fermi gas
• Anomaly in conformal quantum mechanics: From molecular physics to black holes
• An Example of Quantum Anomaly in the Physics of Ultra-Cold Gases
• Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas
• Universal relations for the two-dimensional spin-1/2 Fermi gas with contact interactions
• Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas
• Radio frequency spectra of Feshbach molecules in quasi-two dimensional geometries
• A new insight into BRST anomalies in string theory
• Scale anomalies in non-relativistic field theories in 2+1 dimensions
• Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

Cited by in corpus (8)

• Virial expansion for the Tan contact and Beth-Uhlenbeck formula from 2D SO(2,1) anomalies
• Path-Integral Fujikawa's Approach to Anomalous Virial Theorems and Equations of State for Systems with $SO(2,1)$ Symmetry
• Virial Theorem for Non-relativistic Quantum Fields in D Spatial Dimensions
• A note on broken dilatation symmetry in planar noncommutative theory
• Path-Integral Approach to Scale Anomaly at Finite Temperature
• Dilational Symmetry-Breaking in Thermodynamics
• Relationship between Fujikawa's Method and the Background Field Method for the Scale Anomaly
• Bose and Fermi Statistics and the Regularization of the Nonrelativistic Jacobian for the Scale Anomaly