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A combinatorial perspective on quantum field theory

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	A combinatorial perspective on quantum field theory/ by Karen Yeats.
作者:	Yeats, Karen.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	ix, 120 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Quantum field theory. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-47551-6
ISBN:	9783319475516

A combinatorial perspective on quantum field theory
Yeats, Karen.

A combinatorial perspective on quantum field theory[electronic resource] /by Karen Yeats. - Cham :Springer International Publishing :2017. - ix, 120 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v.152197-1757 ;. - SpringerBriefs in mathematical physics ;v.2..

Part I Preliminaries -- Introduction -- Quantum field theory set up -- Combinatorial classes and rooted trees -- The Connes-Kreimer Hopf algebra -- Feynman graphs -- Part II Dyson-Schwinger equations -- Introduction to Dyson-Schwinger equations -- Sub-Hopf algebras from Dyson-Schwinger equations -- Tree factorial and leading log toys -- Chord diagram expansions -- Differential equations and the (next-to)m leading log expansion -- Part III Feynman periods -- Feynman integrals and Feynman periods -- Period preserving graph symmetries -- An invariant with these symmetries -- Weight -- The c2 invariant -- Combinatorial aspects of some integration algorithms -- Index.

This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author's biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.

ISBN: 9783319475516

Standard No.: 10.1007/978-3-319-47551-6doiSubjects--Topical Terms:

579915
Quantum field theory.

LC Class. No.: QC174.45

Dewey Class. No.: 530.143

A combinatorial perspective on quantum field theory
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505 0 $a Part I Preliminaries -- Introduction -- Quantum field theory set up -- Combinatorial classes and rooted trees -- The Connes-Kreimer Hopf algebra -- Feynman graphs -- Part II Dyson-Schwinger equations -- Introduction to Dyson-Schwinger equations -- Sub-Hopf algebras from Dyson-Schwinger equations -- Tree factorial and leading log toys -- Chord diagram expansions -- Differential equations and the (next-to)m leading log expansion -- Part III Feynman periods -- Feynman integrals and Feynman periods -- Period preserving graph symmetries -- An invariant with these symmetries -- Weight -- The c2 invariant -- Combinatorial aspects of some integration algorithms -- Index.
520 $a This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author's biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.
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