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Graphs in perturbation theoryalgebra...

Borinsky, Michael.

Graphs in perturbation theoryalgebraic structure and asymptotics /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Graphs in perturbation theoryby Michael Borinsky.
其他題名:	algebraic structure and asymptotics /
作者:	Borinsky, Michael.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	xviii, 173 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
標題:	Quantum field theory.
電子資源:	https://doi.org/10.1007/978-3-030-03541-9
ISBN:	9783030035419$q(electronic bk.)

Graphs in perturbation theoryalgebraic 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$q(electronic bk.)

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

203819
Quantum field theory.

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

Dewey Class. No.: 530.1436

Graphs in perturbation theoryalgebraic 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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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.
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