General Dyson-Schwinger equations and systems - Archive ouverte HAL Access content directly
Journal Articles Communications in Mathematical Physics Year : 2014

General Dyson-Schwinger equations and systems

Loïc Foissy


We classify combinatorial Dyson-Schwinger equations giving a Hopf subalgebra of the Hopf algebra of Feynman graphs of the considered Quantum Field Theory. We first treat single equations with an arbitrary number (eventually infinite) of insertion operators. we distinguish two cases; in the first one, the Hopf subalgebra generated by the solution is isomorphic to the Faà di Bruno Hopf algebra or to the Hopf algebra of symmetric functions; in the second case, we obtain the dual of the enveloping algebra of a particular associative algebra (seen as a Lie algebra). We also treat systems with an arbitrary finite number of equations, with an arbitrary number of insertion operators, with at least one of degree 1 in each equation.
Fichier principal
Vignette du fichier
DSE.pdf (290.12 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00651069 , version 1 (12-12-2011)



Loïc Foissy. General Dyson-Schwinger equations and systems. Communications in Mathematical Physics, 2014. ⟨hal-00651069⟩


190 View
111 Download



Gmail Facebook X LinkedIn More