Virial Theorem for Non-relativistic Quantum Fields in D Spatial Dimensions

Abstract

The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in low-dimensional systems. The potential appearance of a Jacobian $J$ due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the $J=1$ case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, $J=1$, is not natural, and the generalization to the case $J\ne 1$ is briefly presented.

6 pages (this version is the published version)

References in corpus (2)

• Energy-pressure relation for low-dimensional gases
• Path-Integral Derivation of the Non-relativistic Scale Anomaly

Cited by in corpus (7)

• 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
• Path-Integral Approach to Scale Anomaly at Finite Temperature
• Dilational Symmetry-Breaking in Thermodynamics
• Bose and Fermi Statistics and the Regularization of the Nonrelativistic Jacobian for the Scale Anomaly
• Relationship between Fujikawa's Method and the Background Field Method for the Scale Anomaly
• Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions