Quantum field theory meets Hopf algebra

Abstract

This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman diagrams, connected diagrams, Green functions, renormalization. The use of Hopf algebra for their definition allows for simple recursive derivations and lead to a correspondence between Feynman diagrams and semi-standard Young tableaux. Reciprocally, these concepts are used as models to derive Hopf algebraic constructions such as a connected coregular action or a group structure on the linear maps from S(V) to V. In most cases, noncommutative analogues are derived.

27 pages, 4 figures. Slightly edited version of the published paper

References in corpus (5)

• Combinatorial Hopf algebras in quantum field theory I
• The Hopf algebra of Feynman graphs in QED
• Combinatorics of n-point functions via Hopf algebra in quantum field theory
• Renormalized Perturbation Theory: A Missing Chapter
• The structure of Green functions in quantum field theory with a general state

Cited by in corpus (4)

• The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems
• Tree expansion in time-dependent perturbation theory
• A novel approach to perturbative calculations for a large class of interacting boson theories
• Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory