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We regulate in Euclidean space the Jacobian under scale transformations fortwo-dimensional nonrelativistic fermions and bosons interacting via contactinteractions and compare the resulting scaling anomalies. For fermions,Grassmannian integration inverts the Jacobian: however, this effect iscancelled by the regularization procedure and a result similar to that ofbosons is attained. We show the independence of the result with respect to theregulating function, and show the robustness of our methods by comparing theprocedure with an effective potential method using both cutoff and$\zeta$-function regularization.

Bose and Fermi Statistics and the Regularization of the Nonrelativistic Jacobian for the Scale Anomaly