Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory

zbMATH Open1231.81041arXiv1008.1471MaRDI QIDQ3114336

Adrian Tanasa

Publication date: 4 February 2012

Abstract: We briefly review the r^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative Grosse-Wulkenhaar model.

Full work available at URL: https://arxiv.org/abs/1008.1471

Mathematics Subject Classification ID

Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Noncommutative geometry methods in quantum field theory (81T75) Connections of Hopf algebras with combinatorics (16T30)

Related Items (2)

On the Hopf algebra strucutre of perturbative quantum field theories ⋮ Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory

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