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The virial theorem for non-relativistic complex fields in $D$ spatialdimensions and with arbitrary many-body potential is derived, usingpath-integral methods and scaling arguments recently developed to analyzequantum anomalies in low-dimensional systems. The potential appearance of aJacobian $J$ due to a change of variables in the path-integral expression forthe partition function of the system is pointed out, although in order to makecontact with the literature most of the analysis deals with the $J=1$ case. Thevirial theorem is recast into a form that displays the effect of microscopicscales on the thermodynamics of the system. From the point of view of thispaper the case usually considered, $J=1$, is not natural, and thegeneralization to the case $J\neq 1$ is briefly presented.

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