Graphs in perturbation theory : algebraic structure and asymptotics /

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Bibliographic Details
Author / Creator:Borinsky, Michael, author.
Imprint:Cham, Switzerland : Springer, 2018.
Description:1 online resource (xviii, 173 pages) : illustrations (some color)
Language:English
Series:Springer theses, 2190-5053
Springer theses,
Subject:
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11737369
Hidden Bibliographic Details
ISBN:9783030035419
3030035417
9783030035426
3030035409
9783030035402
Digital file characteristics:text file PDF
Notes:"Doctoral thesis accepted by the Humboldt-Universität zu Berlin, Germany."
Includes bibliographical references.
Online resource; title from PDF title page (SpringerLink, viewed November 13, 2018).
Summary: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.
Other form:Print version: Borinsky, Michael. Graphs in perturbation theory. Cham, Switzerland : Springer, 2018 3030035409 9783030035402
Standard no.:10.1007/978-3-030-03541-9
10.1007/978-3-030-03

MARC

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245 1 0 |a Graphs in perturbation theory :  |b algebraic structure and asymptotics /  |c Michael Borinsky. 
264 1 |a Cham, Switzerland :  |b Springer,  |c 2018. 
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504 |a Includes bibliographical references. 
588 0 |a Online resource; title from PDF title page (SpringerLink, viewed November 13, 2018). 
505 0 |a 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. 
520 |a 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. 
650 0 |a Quantum field theory.  |0 http://id.loc.gov/authorities/subjects/sh85109461 
650 0 |a Perturbation (Mathematics)  |0 http://id.loc.gov/authorities/subjects/sh85100181 
650 0 |a Hopf algebras.  |0 http://id.loc.gov/authorities/subjects/sh85061931 
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650 7 |a Mathematical physics.  |2 bicssc 
650 7 |a Quantum physics (quantum mechanics & quantum field theory)  |2 bicssc 
650 7 |a Hopf algebras.  |2 fast  |0 (OCoLC)fst00960096 
650 7 |a Perturbation (Mathematics)  |2 fast  |0 (OCoLC)fst01058905 
650 7 |a Quantum field theory.  |2 fast  |0 (OCoLC)fst01085105 
655 4 |a Electronic books. 
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