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From the standard procedure for constructing Feynman vacuum graphs in $\phi^4$ theory from the generating functional $Z$, we find a relation with sets of certain combinatorial matrices, which allows us… Click to show full abstract
From the standard procedure for constructing Feynman vacuum graphs in $\phi^4$ 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.
Journal Title: Journal of Physics A: Mathematical and Theoretical
Year Published: 2018
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