Generating loop graphs via Hopf algebra in quantum field theory

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.

22 pages, LaTeX + AMS + eepic; new section with alternative recursion formula added, further minor changes and corrections

References in corpus (2)

• Quantum field theory and Hopf algebra cohomology
• Combinatorics of n-point functions via Hopf algebra in quantum field theory

Cited by in corpus (5)

• A novel approach to perturbative calculations for a large class of interacting boson theories
• Graph rules for the linked cluster expansion of the Legendre effective action
• Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory
• On the decomposition of connected graphs into their biconnected components
• Hopf algebras and the combinatorics of connected graphs in quantum field theory