Reduction of Feynman integrals to integrals of Schl\"afli functions

S. Srednyak

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arXiv · 1707.09103

Reduction of Feynman integrals to integrals of Schl\"afli functions

S. Srednyak

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Abstract

We show that off-shell perturbative amplitudes with arbitrary number of external lines and complex masses can be reduced to $I$-fold integrals of the generalized Schl\"{a}fli functions, where $I$ is the number of lines in the corresponding vacuum diagram which is independent of the number of external lines. The Schl\"{a}fli functions are obtained as analytic continuation of the volume of the spherical simplex as a function of the hyperplane parameters that define the simplex. These functions have nice and thoroughly studied analytic, geometric and number theoretic properties. They possess Gauss-Manin connection and in conformal case are expressed by iterated integrals. Our representation sheds new light on geometry of particle configuration spaces in perturbation theory.

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S. Srednyak. 2017-07-28. Reduction of Feynman integrals to integrals of Schl\"afli functions. https://arxiv.org/abs/1707.09103

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