Quantum Mechanical Anomalies and the De Witt Effective Action

Topi Kärki; Antti J. Niemi

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arXiv · hep-th/9510198

Quantum Mechanical Anomalies and the De Witt Effective Action

Topi Kärki·Antti J. Niemi

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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.

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Topi Kärki, Antti J. Niemi. 1995-10-26. Quantum Mechanical Anomalies and the De Witt Effective Action. https://arxiv.org/abs/hep-th/9510198

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