Communications in Number Theory and Physics
Volume 16 (2022)
Graphical functions in even dimensions
Pages: 515 – 614
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.
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