English

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

Mathematical Physics 2018-09-06 v2 High Energy Physics - Theory math.MP

Abstract

From the standard procedure for constructing Feynman vacuum graphs in ϕ4\phi^4 theory from the generating functional ZZ, 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.

Keywords

Cite

@article{arxiv.1804.08031,
  title  = {A combinatorial matrix approach for the generation of vacuum Feynman graphs multiplicities in $\phi^4$ theory},
  author = {Erick Castro and Itzhak Roditi},
  journal= {arXiv preprint arXiv:1804.08031},
  year   = {2018}
}

Comments

27 pages