Cohomology of Feynman graphs and perturbative quantum field theory

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dc.creatorIonescu, Lucian M.
dc.date2005-06-08
dc.date.accessioned2026-07-07T05:20:36Z
dc.date.available2026-07-07T05:20:36Z
dc.descriptionAn analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. The graph complex is generated by orientation classes of labeled directed graphs. A graded commutative product is also defined, compatible with the coproduct. Moreover, a dg-Hopf algebra is identified. Graph cohomology is defined applying the cobar construction to the dg-coalgebra structure. As an application, L-infinity morphisms represented as series over Feynman graphs correspond to graph cocycles. Notably the total differential of the cobar construction corresponds to the L-infinity morphism condition. The main example considered is Kontsevich's formality morphism. The relation with perturbative quantum field theory is considered by interpreting L-infinity morphisms as partition functions, and the coefficients of the graph expansions as Feynman integrals.
dc.descriptionDec. 2003, LaTeX, 15 pages; appeared in Focus on Quantum Field Theory, Nova Publishers Inc. 2005
dc.identifierhttps://arxiv.org/abs/math/0506142
dc.identifierhttp://arxiv.org/abs/math/0506142
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75433
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subject18G55; 81Q30
dc.titleCohomology of Feynman graphs and perturbative quantum field theory
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