Graphical functions in even dimensions
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 ϕ4 theory and to order five in six-dimensional ϕ3 theory. In this article we present the theory of graphical functions in even dimensions ≥4 with detailed reviews of known properties and full proofs whenever possible.
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