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.

Michael Borinsky

Oliver Schnetz

Communications in Number Theory and Physics

专注于最广泛意义上的数论在理论物理学中的应用。通过主要发表有关这两个领域之间关系和动态的研究、评论和说明性文章，为数论和理论物理学研究人员之间的交流提供一个论坛。

This journal focuses on the broad applications of number theory in theoretical physics. We primarily publish research, reviews, and expository articles concerning the relationships and dynamics between these two fields, providing a forum for communication among researchers in number theory and theoretical physics.

本期刊专注于数论在理论物理学中的广泛应用。我们主要发表关于这两个领域之间关系和动态的研究、评论和说明性文章，为数论和理论物理学研究人员之间的交流提供一个论坛。

Category	Quartile
数学	3
数学, 数学	3
数学, 应用数学	3
数学, 物理数学物理	3

Graphical functions in even dimensions

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Journal Info

Category	Quartile
PHYSICS, MATHEMATICAL	3