Motivic Galois theory for one-loop Feynman integrals in momentum space
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917511641956352 |
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| author | Mounoud, Ulysse |
| author_facet | Mounoud, Ulysse |
| contents | We develop a motivic framework for Feynman integrals of one-loop graphs in momentum space. Its advantage compared to the already existing framework in Feynman representation is that it naturally includes graphs with cuts. To each such graph, we associate a motivic local system over the space of generic kinematics. Our construction is functorial with respect to the natural operations on graphs: edge contraction and cutting. We compute the weight-graded pieces of the motivic local systems. They are Tate twists of quadratic Artin motives associated with maximally cut quotient graphs. We also derive a formula for the (co)action of the de Rham motivic Galois group, expressed in terms of cut quotient graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20106 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Motivic Galois theory for one-loop Feynman integrals in momentum space Mounoud, Ulysse Algebraic Geometry Number Theory We develop a motivic framework for Feynman integrals of one-loop graphs in momentum space. Its advantage compared to the already existing framework in Feynman representation is that it naturally includes graphs with cuts. To each such graph, we associate a motivic local system over the space of generic kinematics. Our construction is functorial with respect to the natural operations on graphs: edge contraction and cutting. We compute the weight-graded pieces of the motivic local systems. They are Tate twists of quadratic Artin motives associated with maximally cut quotient graphs. We also derive a formula for the (co)action of the de Rham motivic Galois group, expressed in terms of cut quotient graphs. |
| title | Motivic Galois theory for one-loop Feynman integrals in momentum space |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2605.20106 |