Graphical functions in parametric space

Golz, Marcel; Panzer, Erik; Schnetz, Oliver

doi:10.1007/s11005-016-0935-6

Graphical functions in parametric space

Sep 24, 2015

16 pages

Published in:

Lett.Math.Phys. 107 (2017) 6, 1177-1192

Published: Dec 20, 2016

e-Print:

1509.07296 [math-ph]

DOI:

10.1007/s11005-016-0935-6

View in:

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Abstract: (Springer)

Graphical functions are positive functions on the punctured complex plane

{\mathbb C}{\setminus }\{0,1\}

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.

Note:

v2: extended introduction, minor changes in notation and correction of misprints

Perturbation theory
Graphical functions
Feynman integrals
Parametric representation
parametric
field theory
analytic properties
Feynman graph
any-dimensional
ultraviolet

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