Overview

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.

Full Product Details

Author:   Karen Yeats
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   1st ed. 2017
Volume:   15
Dimensions:   Width: 15.50cm , Height: 0.70cm , Length: 23.50cm
Weight:   2.117kg
ISBN:  

9783319475509

ISBN 10:   3319475509
Pages:   120
Publication Date:   22 December 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

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.

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