SCALE ANOMALIES IN NONRELATIVISTIC FIELD-THEORIES IN 2+1 DIMENSIONS

From the one-loop effective potential for a gas of nonrelativistic bos ons in two spatial dimensions interacting via a delta-function potenti al at zero temperature and finite chemical potential, the anomaly of t he energy-momentum tensor follows directly. It is also similarly deriv ed when the bosons have an additional Chem-Simons interaction. In the special case of anyons, the scale anomaly vanishes to one-loop order i n the effective potential and also to second order in the statistical angle.