Virial Theorem for Nonrelativistic Quantum Fields in Spatial Dimensions
Carlos R. Ordóñez (Department of Physics, University of Houston, Houston, TX 77204-5005, USA, Department of Science and Technology, Technological University of Panama, Campus Victor Levi, Panama City, Panama); Chris L. Lin (Department of Physics, University of Houston, Houston, TX 77204-5005, USA)
The virial theorem for nonrelativistic complex fields in 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 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 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, , is not natural, and the generalization to the case is briefly presented.