A chord diagram expansion coming from some Dyson-Schwinger equations

2012/10/19 by Marie, Nicolas, Yeats, Karen · 1 citation
#05A15 #81T99 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1210.5457

Abstract

We give an expression for the solution to propagator-type Dyson-Schwinger equations with one primitive at 1 loop as an expansion over rooted connected chord diagrams. Along the way we give a refinement of a classical recurrence of rooted connected chord diagrams, and a representation in terms of binary trees.

Cited by

• Operads and bialgebras of multi-indices, and Novikov algebras

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• The algebraic structure of Dyson--Schwinger equations with multiple insertion places