arXiv subjects
Publications and source records attributed to Nicholas Olson-Harris.
We give combinatorially controlled series solutions to Dyson--Schwinger equations with multiple insertion places using tubings of rooted trees and investigate the algebraic relation between such solutions and the renormalization group equation.
We give series solutions to single insertion place propagator-type systems of Dyson--Schwinger equations using binary tubings of rooted trees. These solutions are combinatorially transparent in the sense that each tubing has a straightforward contribution. The Dyson--Schwinger equations solved here are more general than those previously solved by chord diagram techniques, including systems and non-integer values of the insertion parameter $s$. We remark on interesting combinatorial connections and properties.