NONRELATIVISTIC FIELD-THEORETIC SCALE ANOMALY

Abstract

We construct a nonrelativistic scalar field theory with a quartic self-interaction in 2 + 1 dimensions as an infinite mass limit of a relativistic theory, and calculate the two-particle scattering amplitude and two-particle bound-state energy. We show that the results are the same as for quantum mechanics of two scalar particles interacting via a delta-function potential. Renormalization of the theory reveals an anomalous breaking of scale symmetry. The renormalization group structure is presented and the anomaly is expressed in terms of the trace of the energy-momentum tensor.