Graphs in Perturbation Theory: Algebraic Structure and Asymptotics

Description

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. Front Matter ....Pages i-xviii Introduction (Michael Borinsky)....Pages 1-12 Graphs (Michael Borinsky)....Pages 13-25 Graphical Enumeration (Michael Borinsky)....Pages 27-46 The Ring of Factorially Divergent Power Series (Michael Borinsky)....Pages 47-81 Coalgebraic Graph Structures (Michael Borinsky)....Pages 83-107 The Hopf Algebra of Feynman Diagrams (Michael Borinsky)....Pages 109-134 Examples from Zero-Dimensional QFT (Michael Borinsky)....Pages 135-172 Back Matter ....Pages 173-173