A combinatorial matrix approach for the generation of vacuum Feynman graphs multiplicities in ϕ4 theory. (30th August 2018)

• Record Type: Journal Article
• Authors: Castro, E; Roditi, I
• Is Part Of: Journal of physics. Volume 51:Number 39(2018)
• Publication Date: 2018-08-30
• Subjects: Feynman vacuum diagrams -- ϕ4 theory -- counting graphs -- combinatorial matrix theory; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aad9b4
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: From the standard procedure for constructing Feynman vacuum graphs in 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 Feynman vacuum graphs and their multiplicities.