Spitzer's identity and the algebraic Birkhoff decomposition in pQFT

2004/07/11 by Kurusch Ebrahimi-Fard, Li Guo, Dirk Kreimer · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.CO #math.MP #math.RA

paper · pdf · doi:10.1088/0305-4470/37/45/020

published as J.Phys. A37 (2004) 11037-11052 · 19 pages, 2 figures

arxiv created 2004/07/11 · openalex publication_date 2004/10/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

In this paper we continue to explore the notion of Rota–Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theory. We show in very simple algebraic terms that the solutions of the recursively defined formulae for the Birkhoff factorization of regularized Hopf algebra characters, i.e. Feynman rules, naturally give a non-commutative generalization of the well-known Spitzer's identity. The underlying abstract algebraic structure is analysed in terms of complete filtered Rota–Baxter algebras.

Citations

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem

Cited by

• Functional representations of integrable hierarchies
• Combinatorics of renormalization as matrix calculus