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Graphs in perturbation theory = algebraic structure and asymptotics /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Graphs in perturbation theory/ by Michael Borinsky.
Reminder of title:	algebraic structure and asymptotics /
Author:	Borinsky, Michael.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xviii, 173 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Quantum field theory. -
Online resource:	https://doi.org/10.1007/978-3-030-03541-9
ISBN:	9783030035419

Graphs in perturbation theory = algebraic structure and asymptotics /
Borinsky, Michael.

Graphs in perturbation theoryalgebraic structure and asymptotics /[electronic resource] :by Michael Borinsky. - Cham :Springer International Publishing :2018. - xviii, 173 p. :ill. (some col.), digital ;24 cm. - Springer theses,2190-5053. - Springer theses..

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.

ISBN: 9783030035419

Standard No.: 10.1007/978-3-030-03541-9doiSubjects--Topical Terms:

579915
Quantum field theory.

LC Class. No.: QC174.45 / .B675 2018

Dewey Class. No.: 530.1436

Graphs in perturbation theory = algebraic structure and asymptotics /
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245 1 0 $a Graphs in perturbation theory $h [electronic resource] : $b algebraic structure and asymptotics / $c by Michael Borinsky.
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300 $a xviii, 173 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Springer theses, $x 2190-5053
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. $3 579915
650 0 $a Perturbation (Mathematics) $3 528258
650 1 4 $a Mathematical Methods in Physics. $3 670749
650 2 4 $a Applications of Graph Theory and Complex Networks. $3 1113468
650 2 4 $a Graph Theory. $3 786670
650 2 4 $a Elementary Particles, Quantum Field Theory. $3 672693
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950 $a Physics and Astronomy (Springer-11651)