Quantum Mechanical Anomalies and the De Witt Effective Action
Abstract
Description
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)
10 pages, standard Latex run twice (3 figures that run under stadard Latex)