Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory
arXiv:1001.3567 · doi:10.1063/1.3449321
Abstract
We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle irreducible n-point function in terms of its loop order contributions. The algebraic representation is so that graphs can be evaluated as Feynman graphs.