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arXiv · 2105.05015

Graphical functions in even dimensions

Michael Borinsky·Oliver Schnetz
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Abstract

Graphical functions are special position space Feynman integrals, which can be used to calculate Feynman periods and one- or two-scale processes at high loop orders. With graphical functions, renormalization constants have been calculated to loop orders seven and eight in four-dimensional $\phi^4$ theory and to order five in six-dimensional $\phi^3$ theory. In this article we present the theory of graphical functions in even dimensions $\geq4$ with detailed reviews of known properties and full proofs whenever possible.

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Michael Borinsky, Oliver Schnetz. 2021-05-11. Graphical functions in even dimensions. https://doi.org/10.4310/cntp.2022.v16.n3.a3

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