Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
arXiv:1008.1471
Abstract
We briefly review the rôle 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.
15 pages, 6 figures
References in corpus (9)
- Group field theory with non-commutative metric variables
- Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology
- Vacuum configurations for renormalizable non-commutative scalar models
- Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
- Mixed Hodge Structures and Renormalization in Physics
- Non-Commutative Complete Mellin Representation for Feynman Amplitudes
- Overview of the parametric representation of renormalizable non-commutative field theory
- Feynman amplitudes in renormalizable non-commutative quantum field theory
- Lie subalgebras of the Weyl algebra. Lie algebras of order 3 and their application to cubic supersymmetry