A combinatorial matrix approach for the generation of vacuum Feynman graphs multiplicities in $\phi^{4}$ theory

DOI10.1088/1751-8121/aad9b4zbMath1407.81120arXiv1804.08031OpenAlexW2798432156MaRDI QIDQ3119963

E. R. Castro, Itzhak Roditi

Publication date: 28 February 2019

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

Full work available at URL: https://arxiv.org/abs/1804.08031

zbMATH Keywords

combinatorial matrix theory\(\phi^4\) theorycounting graphsFeynman vacuum diagrams

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Enumeration in graph theory (05C30) Feynman diagrams (81T18) Connections of Hopf algebras with combinatorics (16T30)

Related Items

Permutation invariant Gaussian two-matrix models, A recursive enumeration of connected Feynman diagrams with an arbitrary number of external legs in the fermionic non-relativistic interacting gas, Quantum mechanics of bipartite ribbon graphs: integrality, lattices and Kronecker coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Combinatorics of (perturbative) quantum field theory
• A novel approach to perturbative calculations for a large class of interacting boson theories
• Automatic Feynman graph generation
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Enumeration of \(N\)-rooted maps using quantum field theory
• Symmetry factors of Feynman diagrams for scalar fields
• Counting tensor model observables and branched covers of the 2-sphere
• Quantum field theory and the coloring problem of graphs
• Analytic solution of Hedin’s equations in zero dimensions
• Equivalence between the Arquès-Walsh sequence formula and the number of connected Feynman diagrams for every perturbation order in the fermionic many-body problem
• Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Padé-Borel resummation.