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A geometrical angle of Feynman integrals
journal contribution
posted on 2023-05-16, 11:05 authored by Davydychev, AI, Robert DelbourgoRobert DelbourgoA direct link between a one-loop N-point Feynman diagram and a geometrical representation based on the N-dimensional simplex is established by relating the Feynman parametric representations to the integrals over contents of (N - 1)-dimensional simplices in non-Euclidean geometry of constant curvature. In particular, the four-point function in four dimensions is proportional to the volume of a three-dimensional spherical (or hyperbolic) tetrahedron which can be calculated by splitting into birectangular ones. It is also shown that the known formula of reduction of the N-point function in (N - 1) dimensions corresponds to splitting the related N-dimensional simplex into N rectangular ones. © 1998 American Institute of Physics.
History
Publication title
Journal of Mathematical PhysicsVolume
39Issue
9Pagination
4299-4334ISSN
0022-2488Department/School
School of Natural SciencesPublisher
American Institute of PhysicsPlace of publication
Circulation & Fulfillment Div, 2 Huntington Quadrangle, Ste 1 N O 1, Melville, USA, Ny, 11747-4501Repository Status
- Restricted