The signed permutation group on Feynman graphs

DOI10.1063/1.4961517zbMath1350.81024arXiv1512.02408OpenAlexW2189864779MaRDI QIDQ2820908

Julian Purkart

Publication date: 12 September 2016

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

Full work available at URL: https://arxiv.org/abs/1512.02408

zbMATH Keywords

graph theorypermutation groupFeynman rulesFeynman integralsHopf algebar

Mathematics Subject Classification ID

Trees (05C05) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Symmetric groups (20B30) Hopf algebras and their applications (16T05)

Cites Work

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• Angles, scales and parametric renormalization
• Algebraic lattices in QFT renormalization
• Filtrations in Dyson-Schwinger equations: Next-to\(^{\{j \}}\)-leading log expansions systematically
• Anatomy of a gauge theory
• Hopf algebras, renormalization and noncommutative geometry
• On the Hopf algebra strucutre of perturbative quantum field theories
• The Hopf algebras of decorated rooted trees. I
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Quantization of gauge fields, graph polynomials and graph homology
• Renormalization of gauge fields: a Hopf algebra approach
• FEYNMAN GRAPH POLYNOMIALS
• The Hopf algebra approach to Feynman diagram calculations