Virial Theorem for Nonrelativistic Quantum Fields in D Spatial Dimensions

Abstract EN

The virial theorem for nonrelativistic complex fields in D spatialdimensions 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 potentialappearance 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 ≠ 1 is briefly presented.