Spectral Decomposition of Euler-Mellin Integrals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915291875770368 |
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| author | Helmer, Martin Tellander, Felix |
| author_facet | Helmer, Martin Tellander, Felix |
| contents | We consider the spectral decomposition of singularities of integrals and their integrands. Our results apply to any integral of Euler-Mellin type, and thus especially to every scalar Feynman integral. Specifically we provide for both the integrand and integral respectively; two explicit constructions of the characteristic variety and characteristic cycle of the constructible function and $D$-module they are associated with. From this we also obtain the singular locus or Landau singularities of the integral. En route we give a simple procedure to compute the local Euler obstruction function of a variety, and using this, to compute the Euler characteristic of the complex link of a Whitney stratum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Decomposition of Euler-Mellin Integrals Helmer, Martin Tellander, Felix Mathematical Physics High Energy Physics - Theory Algebraic Geometry We consider the spectral decomposition of singularities of integrals and their integrands. Our results apply to any integral of Euler-Mellin type, and thus especially to every scalar Feynman integral. Specifically we provide for both the integrand and integral respectively; two explicit constructions of the characteristic variety and characteristic cycle of the constructible function and $D$-module they are associated with. From this we also obtain the singular locus or Landau singularities of the integral. En route we give a simple procedure to compute the local Euler obstruction function of a variety, and using this, to compute the Euler characteristic of the complex link of a Whitney stratum. |
| title | Spectral Decomposition of Euler-Mellin Integrals |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2505.12458 |