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arXiv · 2601.08686

On equivalent methods for functional determinants

Matthias Carosi
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Abstract

Computing functional determinants of differential operators is central to any field-theoretical calculation relying on a saddle-point expansion. A variety of approaches is available for the computation that avoid having to know the eigenspectrum of the operator, and in particular the Gel'fand-Yaglom theorem and the Green's function method. In this note, we show how both approaches can be constructed using a contour integral argument and conclude that these are completely equivalent for computing ratios of determinants of one-dimensional operators. Furthermore, we comment on the presence of vanishing as well as negative eigenvalues and show how the Green's function method provides a natural prescription for handling them.

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Matthias Carosi. 2026-01-13. On equivalent methods for functional determinants. https://doi.org/10.1007/jhep06(2026)073

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