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

Abstract

From the standard procedure for constructing Feynman vacuum graphs in ${\varphi }^4$ theory from the generating functional $Z$, we find a relation with sets of certain combinatorial matrices, which allows us to generate the set of all Feynman graphs and the respective multiplicities in an equivalent combinatoric way. These combinatorial matrices are explicitly related with the permutation group, which facilitates the construction of the vacuum Feynman graphs. Various insights in this combinatoric problem are proposed, which in principle provide an efficient way to compute the Feynman vacuum graphs and its multiplicities.

arXiv comment27 pages

References in corpus (10)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Counting Tensor Model Observables and Branched Covers of the 2-Sphere
• Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Pade-Borel resummation
• Combinatorics of (perturbative) quantum field theory
• Recursive Graphical Construction of Feynman Diagrams and Their Multiplicities in phi^4- and in phi^2A-Theory
• Strings from Feynman Graph counting : without large N
• Hedin's equations and enumeration of Feynman's diagrams
• Symmetry Factors of Feynman Diagrams for Scalar Fields
• A novel approach to perturbative calculations for a large class of interacting boson theories
• Equivalence between the Arquès-Walsh sequence formula and the number of connected Feynman diagrams for every perturbation order in the fermionic many-body problem

Cited by in corpus (1)

• Permutation invariant Gaussian 2-matrix models