TL;DR
This paper develops methods to compute regularized determinants of fluctuation operators, linking them to eigenmodes, and applies these to tunnel determinants in various models, revealing a supersymmetric structure.
Contribution
It introduces a new approach to compute tunnel determinants using eigenmodes, demonstrating their connection to supersymmetric quantum mechanics.
Findings
Computed tunnel determinants for several models
Established a link between fluctuation operators and supersymmetry
Provided a framework for analyzing fluctuation determinants in higher dimensions
Abstract
Methods for computing the regularized determinants of fluctuation operators are being developed. The results follow from the fact that these determinants can be expressed by eigenmodes of the fluctuation operator. As an application the tunnel determinants of some one- and higher-dimensional models are computed. It is shown that every fluctuation operator defines a supersymmetric quantum mechanical system.
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