Graphical functions in parametric space
Marcel Golz, Erik Panzer, Oliver Schnetz
TL;DR
This paper extends the mathematical understanding of graphical functions in quantum field theory by providing a parametric integral representation and a dual graph relation, establishing their real analyticity.
Contribution
It generalizes existing integral representations of graphical functions and introduces a dual graph formula, advancing theoretical insights in quantum field theory mathematics.
Findings
Established a generalized parametric integral representation.
Proved the real analyticity of graphical functions.
Derived a dual graph relation formula.
Abstract
Graphical functions are positive functions on the punctured complex plane which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and Nakanishi, which implies the real analyticity of graphical functions. Moreover we prove a formula that relates graphical functions of planar dual graphs.
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