Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory

Details Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory

2010-01-20

arxiv.org/abs/1001.3567v2

J.Math.Phys.51:082302,2010

Physics

Mathematical Physics

Scientific paper

10.1063/1.3449321

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.

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