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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.08686 |
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| _version_ | 1866917199685353472 |
|---|---|
| author | Carosi, Matthias |
| author_facet | Carosi, Matthias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08686 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On equivalent methods for functional determinants Carosi, Matthias High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics Quantum Physics 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. |
| title | On equivalent methods for functional determinants |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2601.08686 |