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024 7 $a10.1007/978-3-030-03541-9
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035   $a(MiAaPQ)EBC5592906
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100   $a20181104d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aGraphs in Perturbation Theory $eAlgebraic Structure and Asymptotics /$fby Michael Borinsky
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (xviii, 173 pages) $cillustrations
225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053
311   $a3-030-03540-9 
327   $aIntroduction -- Graphs -- Graphical enumeration -- The ring of factorially divergent power series -- Coalgebraic graph structures -- The Hopf algebra of Feynman diagrams -- Examples from zero-dimensional QFT.
330   $aThis book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.
410  0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053
606   $aPhysics
606   $aGraph theory
606   $aElementary particles (Physics)
606   $aQuantum field theory
606   $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013
606   $aApplications of Graph Theory and Complex Networks$3https://scigraph.springernature.com/ontologies/product-market-codes/P33010
606   $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020
606   $aElementary Particles, Quantum Field Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P23029
615  0$aPhysics.
615  0$aGraph theory.
615  0$aElementary particles (Physics).
615  0$aQuantum field theory.
615 14$aMathematical Methods in Physics.
615 24$aApplications of Graph Theory and Complex Networks.
615 24$aGraph Theory.
615 24$aElementary Particles, Quantum Field Theory.
676   $a530.143
700   $aBorinsky$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut$0835242
906   $aBOOK
912   $a9910300547103321
996   $aGraphs in Perturbation Theory$92498790
997   $aUNINA