A Combinatorial Perspective on Quantum Field Theory
Springer International Publishing (Verlag)
978-3-319-47550-9 (ISBN)
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.
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.
| Erscheinungsdatum | 03.01.2017 |
|---|---|
| Reihe/Serie | SpringerBriefs in Mathematical Physics |
| Zusatzinfo | IX, 120 p. 16 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Naturwissenschaften ► Physik / Astronomie ► Thermodynamik | |
| Schlagworte | c2 invariant • chord diagram expansion • combinatorial classes • combinatorial Hopf algebras • Connes-Kreimer Hopf algebra • Discrete Mathematics • Dyson-Schwinger equations • Feynman graphs • Feynman periods • graph theory • leading log expansion • Mathematical Physics • Physics • Physics and Astronomy • Quantum Field Theories, String Theory • rooted trees • Schnetz twist • Statistical Physics • sub Hopf algebras • the zigzag result |
| ISBN-10 | 3-319-47550-9 / 3319475509 |
| ISBN-13 | 978-3-319-47550-9 / 9783319475509 |
| Zustand | Neuware |
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