Hopf algebras and the combinatorics of connected graphs in quantum field theory

Abstract

In this talk, we are concerned with the formulation and understanding of the combinatorics of time-ordered n-point functions in terms of the Hopf algebra of field operators. Mathematically, this problem can be formulated as one in combinatorics or graph theory. It consists in finding a recursive algorithm that generates all connected graphs in their Hopf algebraic representation. This representation can be used directly and efficiently in evaluating Feynman graphs as contributions to the n-point functions.Comment: 10 pages, 2 figures, LaTeX + AMS + eepic; to appear in the proceedings of the Conference on Combinatorics and Physics, MPIM Bonn, March 19-23, 200