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A geometrical angle of Feynman integrals


Davydychev, AI and Delbourgo, R, A geometrical angle of Feynman integrals, Journal of Mathematical Physics, 39, (9) pp. 4299-4334. ISSN 0022-2488 (1998) [Refereed Article]

DOI: doi:10.1063/1.532513


A 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.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Other physical sciences
Research Field:Other physical sciences not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Davydychev, AI (Mr Andrei Davydychev)
UTAS Author:Delbourgo, R (Professor Robert Delbourgo)
ID Code:13369
Year Published:1998
Web of Science® Times Cited:67
Deposited By:Physics
Deposited On:1998-08-01
Last Modified:2011-08-08

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