Quantum Mechanical Anomalies and the De Witt Effective Action

Abstract

We study the partition function of N=1 supersymmetric De Rham quantum mechanics on a Riemannian manifold, with a nontrivial chemical potential $μ$ for the fermions. General arguments suggest that when $μ\to \infty$ we should get the partition function of a free point particle. We investigate this limit by exact evaluation of the fermionic path integral. In even dimensions we find the De Witt term with a definite numerical factor. However, in odd dimensions our result is pestered by a quantum mechanical anomaly and the numerical factor in the De Witt term remains ambiquous.

10 pages, standard Latex run twice (3 figures that run under stadard Latex)