Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology

Abstract

In this review we discuss the relevance of the Hochschild cohomology of renormalization Hopf algebras for local quantum field theories and their equations of motion.

arXiv comment29 pages, eps figures; minor changes; final version

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• Algebraic structures in quantum gravity
• Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
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• The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras
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• Filtrations in Dyson-Schwinger equations: next-to^{j} -leading log expansions systematically
• Hopf algebras and Dyson-Schwinger equations
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• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory
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