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

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3449321· OSTI ID:21476530

Mestre, Angela ^[1]

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1. Institut de Mineralogie et de Physique des Milieux Condenses, CNRS UMR 7590, Universites Paris 6 et 7, IPGP, 140 rue de Lourmel, 75015 Paris (France)

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.

• OSTI ID: 21476530
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 8; Other Information: DOI: 10.1063/1.3449321; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
COMMUTATION RELATIONS
FEYNMAN DIAGRAM
GRAPH THEORY
QUANTUM FIELD THEORY
VERTEX FUNCTIONS
DIAGRAMS
FIELD THEORIES
FUNCTIONS
INFORMATION
MATHEMATICS