Type: Article

Generating loop graphs via Hopf algebra in quantum field theory

Angela Mestre; Robert Oeckl;

Abstract:

We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number.