03547nam 22005775 450 991030054710332120200630220814.03-030-03541-710.1007/978-3-030-03541-9(CKB)4100000007110750(MiAaPQ)EBC5592906(DE-He213)978-3-030-03541-9(PPN)232468974(EXLCZ)99410000000711075020181104d2018 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGraphs in Perturbation Theory Algebraic Structure and Asymptotics /by Michael Borinsky1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (xviii, 173 pages) illustrationsSpringer Theses, Recognizing Outstanding Ph.D. Research,2190-50533-030-03540-9 Introduction -- Graphs -- Graphical enumeration -- The ring of factorially divergent power series -- Coalgebraic graph structures -- The Hopf algebra of Feynman diagrams -- Examples from zero-dimensional QFT.This book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5053PhysicsGraph theoryElementary particles (Physics)Quantum field theoryMathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Applications of Graph Theory and Complex Networkshttps://scigraph.springernature.com/ontologies/product-market-codes/P33010Graph Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M29020Elementary Particles, Quantum Field Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P23029Physics.Graph theory.Elementary particles (Physics).Quantum field theory.Mathematical Methods in Physics.Applications of Graph Theory and Complex Networks.Graph Theory.Elementary Particles, Quantum Field Theory.530.143Borinsky Michaelauthttp://id.loc.gov/vocabulary/relators/aut835242BOOK9910300547103321Graphs in Perturbation Theory2498790UNINA