Combinatorics of n-point functions via Hopf algebra in quantum field theory

Abstract

We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more intrinsic and leads to efficient algorithms suitable for concrete computations. It may also be used to efficiently perform tree level computations.

26 pages, LaTeX + AMS + eepic; minor corrections and modifications

References in corpus (4)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• On the Hopf algebraic origin of Wick normal-ordering
• Braided Quantum Field Theory
• Quantum field theory and Hopf algebra cohomology

Cited by in corpus (7)

• Quantum field theory meets Hopf algebra
• Generating loop graphs via Hopf algebra in quantum field theory
• The combinatorics of Green's functions in planar field theories
• Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory
• On the decomposition of connected graphs into their biconnected components
• Generating connected and biconnected graphs
• Hopf algebras and the combinatorics of connected graphs in quantum field theory