Graphical functions in even dimensions

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 $\geq 4$ with detailed reviews of known properties and full proofs whenever possible.

2010 Mathematics Subject Classification

Primary 81Q15, 81Q30. Secondary 81T99.

Full Text (PDF format)

M.B. was supported by NWO Vidi grant 680-47-551.

O.S. was supported by DFG grant SCHN 1240/3.

Received 11 May 2021

Accepted 4 May 2022

Published 4 October 2022