Knots and Feynman Diagrams.pdf

Knots and Feynman Diagrams PDF

Dirk Kreimer

This book provides an accessible and up-to-date introduction to how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory.Beginning with a summary of key ideas from perturbative quantum field theory and an introduction to the Hopf algebra structure of renormalisation, early chapters discuss the rationality of ladder diagrams and simple link diagrams. The necessary basics of knot theory are then presented and the number-theoretic relationship between the topology of Feynman diagrams and knot theory is explored. Later chapters discuss four-term relations motivated by the discovery of Vassiliev invariants in knot theory and draw a link to algebraic structures recently observed in noncommutative geometry. Detailed references are included.Dealing with material at perhaps the most productive interface between mathematics and physics, the book will not only bc of considerable interest to theoretical and particle physicists, but also to many mathematicians.

KNOTS AND FEYNMAN DIAGRAMS SIYANG LING Contents 1. Introduction 1 2. Knots 1 2.1. Isotopic Knots 1 2.2. States and the Bracket Polynomial 3 2.3. Jones Polynomial 5 3. Knots and Feynman Diagrams 5 3.1. Knot Diagrams as Abstract Tensors 5 3.2. Unitarity and Yang-Baxter Equation 6 3.3. Interaction and Annihilation/Creation 7 3.4. Formal Feynman Diagrams 8 References 9 1. Introduction Knots … 0521587611 - Knots and Feynman Diagrams …

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9780521587617 ISBN
Knots and Feynman Diagrams.pdf


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