The uses of Connes and Kreimer's algebraic formulation of renormalization theory

Abstract

We show how, modulo the distinction between the antipode and the "twisted" or "renormalized" antipode, Connes and Kreimer's algebraic paradigm trivializes the proofs of equivalence of the (corrected) Dyson-Salam, Bogoliubov-Parasiuk-Hepp and Zimmermann procedures for renormalizing Feynman amplitudes. We discuss the outlook for a parallel simplification of computations in quantum field theory, stemming from the same algebraic approach.

arXiv comment15 pages, Latex. Minor changes, typos fixed, 2 references added

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Cited by in corpus (6)

• Combinatorial Hopf algebras in quantum field theory I
• Hopf algebra approach to Feynman diagram calculations
• An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions
• Matrix Representation of Renormalization in Perturbative Quantum Field Theory
• Separable representations of higher-rank graphs
• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory