The Analytic Evolution of Dyson–Schwinger Equations via Homomorphism Densities Article - 2021

Ali Shojaei-Fard

Ali Shojaei-Fard, « The Analytic Evolution of Dyson–Schwinger Equations via Homomorphism Densities  », Math.Phys.Anal.Geom., 2021, p. 18

Abstract

Feynman graphon representations of Feynman diagrams lead us to build a new separable Banach space $\mathcal S^\Phi ,g_\approx$ originated from the collection of all Dyson–Schwinger equations in a given (strongly coupled) gauge field theory $\Phi$ with the bare coupling constant $g$. We study the Gâteaux differential calculus on the space of functionals on $\mathcal S^\Phi ,g_\approx$ in terms of a new class of homomorphism densities. We then show that Taylor series representations of smooth functionals on $\mathcal S^\Phi ,g_\approx$ provide a new analytic description for solutions of combinatorial Dyson–Schwinger equations.