A Combinatorial Perspective on Quantum Field Theory

• Main Author: Yeats, Karen (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: SpringerBriefs in Mathematical Physics, 15
• Subjects: Physics.; Discrete mathematics.; Mathematical physics.; Quantum field theory.; String theory.; Quantum Field Theories, String Theory.; Mathematical Physics.; Discrete Mathematics.

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...

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.