Self-duality of massless scalar three-point amplitudes
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918468825120768 |
|---|---|
| author | Schnetz, Oliver |
| author_facet | Schnetz, Oliver |
| contents | We prove that off-shell massless scalar three-point Feynman integrals are self-dual under Fourier transformation. This implies that a momentum space integral can be expressed as the position space integral of the same Feynman graph with transformed edge-weights (not the dual graph) if external vertices are labeled accordingly. In particular, any off-shell massless scalar three-point Feynman integral can be expressed as a graphical function. The result follows immediately from a theorem by M. Golz, E. Panzer and the author on parametric representations of position space integrals (2015), but it was only observed by X. Jiang in 2025 in the context of four-dimensional $\mathcal{N}=4$ Super-Yang-Mills theory. We generalize Jiang's result and discuss the consequences of the self-duality in the context of graphical functions. In particular, we derive a new identity for graphical functions and a new twist relation for scalar integrals (Feynman periods) in $ϕ^4$ theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21057 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Self-duality of massless scalar three-point amplitudes Schnetz, Oliver High Energy Physics - Theory High Energy Physics - Phenomenology We prove that off-shell massless scalar three-point Feynman integrals are self-dual under Fourier transformation. This implies that a momentum space integral can be expressed as the position space integral of the same Feynman graph with transformed edge-weights (not the dual graph) if external vertices are labeled accordingly. In particular, any off-shell massless scalar three-point Feynman integral can be expressed as a graphical function. The result follows immediately from a theorem by M. Golz, E. Panzer and the author on parametric representations of position space integrals (2015), but it was only observed by X. Jiang in 2025 in the context of four-dimensional $\mathcal{N}=4$ Super-Yang-Mills theory. We generalize Jiang's result and discuss the consequences of the self-duality in the context of graphical functions. In particular, we derive a new identity for graphical functions and a new twist relation for scalar integrals (Feynman periods) in $ϕ^4$ theory. |
| title | Self-duality of massless scalar three-point amplitudes |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2602.21057 |