Hepp’s bound for Feynman graphs and matroids
We study a rational matroid invariant, obtained as the tropicalization of the Feynman period integral. It equals the volume of the polar of the matroid polytope and we give efficient formulas for its computation. This invariant is proven to respect all known identities of Feynman integrals for graph...
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| Format: | Journal article |
| Language: | English |
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European Mathematical Society
2022
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| _version_ | 1826310411717181440 |
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| author | Panzer, E |
| author_facet | Panzer, E |
| author_sort | Panzer, E |
| collection | OXFORD |
| description | We study a rational matroid invariant, obtained as the tropicalization of the Feynman period integral. It equals the volume of the polar of the matroid polytope and we give efficient formulas for its computation. This invariant is proven to respect all known identities of Feynman integrals for graphs. We observe a strong correlation between the tropical and transcendental integrals, which yields a method to approximate unknown Feynman periods. |
| first_indexed | 2024-03-07T07:51:52Z |
| format | Journal article |
| id | oxford-uuid:83ae2c7f-1c0a-4fbf-80e3-1530732933b3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:51:52Z |
| publishDate | 2022 |
| publisher | European Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:83ae2c7f-1c0a-4fbf-80e3-1530732933b32023-07-21T11:09:54ZHepp’s bound for Feynman graphs and matroidsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:83ae2c7f-1c0a-4fbf-80e3-1530732933b3EnglishSymplectic ElementsEuropean Mathematical Society2022Panzer, EWe study a rational matroid invariant, obtained as the tropicalization of the Feynman period integral. It equals the volume of the polar of the matroid polytope and we give efficient formulas for its computation. This invariant is proven to respect all known identities of Feynman integrals for graphs. We observe a strong correlation between the tropical and transcendental integrals, which yields a method to approximate unknown Feynman periods. |
| spellingShingle | Panzer, E Hepp’s bound for Feynman graphs and matroids |
| title | Hepp’s bound for Feynman graphs and matroids |
| title_full | Hepp’s bound for Feynman graphs and matroids |
| title_fullStr | Hepp’s bound for Feynman graphs and matroids |
| title_full_unstemmed | Hepp’s bound for Feynman graphs and matroids |
| title_short | Hepp’s bound for Feynman graphs and matroids |
| title_sort | hepp s bound for feynman graphs and matroids |
| work_keys_str_mv | AT panzere heppsboundforfeynmangraphsandmatroids |