Renormalization of gauge fields: A Hopf algebra approach

Abstract

We study the Connes-Kreimer Hopf algebra of renormalization in the case of gauge theories. We show that the Ward identities and the Slavnov-Taylor identities (in the abelian and non-abelian case respectively) are compatible with the Hopf algebra structure, in that they generate a Hopf ideal. Consequently, the quotient Hopf algebra is well-defined and has those identities built in. This provides a purely combinatorial and rigorous proof of compatibility of the Slavnov-Taylor identities with renormalization.

24 pages; uses feynmf

References in corpus (1)

• The Hopf algebra of Feynman graphs in QED

Cited by in corpus (10)

• Recursive relations in the core Hopf algebra
• Exponential renormalization
• Recursion and growth estimates in renormalizable quantum field theory
• Growth estimates for Dyson-Schwinger equations
• Feynman integrals and motives
• Algebraic Structures in local QFT
• Algebra for quantum fields
• Renormalization of Gauge theories and the Hopf Algebra of Diagrams
• Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations
• Computations and generation of elements on the Hopf algebra of Feynman graphs