The structure of renormalization Hopf algebras for gauge theories. I: Representing Feynman graphs on BV-algebras

DOI10.1007/s00220-009-0829-xzbMath1207.81083arXiv0807.0999OpenAlexW2135766735MaRDI QIDQ1048052

Walter D. van Suijlekom

Publication date: 11 January 2010

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.0999

zbMATH Keywords

Hopf algebrasrenormalizationgauge theoryBatalin-Vilkovisky algebras

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Constructive quantum field theory (81T08) Bialgebras (16T10)

Related Items (16)

The QCD \(\beta \)-function from global solutions to Dyson-Schwinger equations ⋮ Gauge symmetries and renormalization ⋮ Log expansions from combinatorial Dyson-Schwinger equations ⋮ Hopf-algebraic renormalization of QED in the linear covariant gauge ⋮ Quantization of gauge fields, graph polynomials and graph homology ⋮ Recursive relations in the core Hopf algebra ⋮ Polynomial functors and combinatorial Dyson–Schwinger equations ⋮ Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees. ⋮ The bialgebra of specified graphs and external structures ⋮ Rearranging Dyson-Schwinger equations ⋮ The dynamics of non-perturbative phases via Banach bundles ⋮ Character groups of Hopf algebras as infinite-dimensional Lie groups ⋮ Gravity-Matter Feynman Rules for any Valence ⋮ Faà di Bruno for operads and internal algebras ⋮ Perturbative renormalisation for not-quite-connected bialgebras ⋮ On the pre-Lie algebra of specified Feynman graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-commutative Hopf algebra of formal diffeomorphisms.
• Anatomy of a gauge theory
• Mixed Hodge structures and renormalization in physics
• The QED \(\beta \)-function from global solutions to Dyson-Schwinger equations
• On the Hopf algebra strucutre of perturbative quantum field theories
• On the renormalization group in curved spacetime
• Microlocal analysis and interacting quantum field theories: renormalization on physical back\-grounds.
• The Hopf algebra of rooted trees in Epstein-Glaser renormalization
• Local BRST cohomology in the antifield formalism. I: General theorems
• Local BRST cohomology in the antifield formalism. II: Application to Yang-Mills theory
• Are nonrenormalizable gauge theories renormalizable?
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• The cohomology structure of an associative ring
• Renormalization of gauge fields: a Hopf algebra approach
• A remark on quantum gravity
• Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations.
• An algebraic Birkhoff decomposition for the continuous renormalization group
• Multiplicative Renormalization and Hopf Algebras
• RENORMALIZED QUANTUM YANG–MILLS FIELDS IN CURVED SPACETIME
• Renormalization of gauge fields using Hopf algebras
• Removal of divergences with the Batalin-Vilkovisky formalism
• Quantum Electrodynamics at Small Distances
• Renormalization of QED with planar binary trees
• Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group.
• The Hopf algebra structure of Connes and Kreimer in Epstein-Glaser renormalization

This page was built for publication: The structure of renormalization Hopf algebras for gauge theories. I: Representing Feynman graphs on BV-algebras