Knots and Feynman Diagrams

Author: Dirk Kreimer Series: Cambridge Lecture Notes in Physics

Up-to-date introduction to applications of knot theory and Feynman diagrams to quantum field theory.

This volume explains how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. The author emphasizes how new discoveries in mathematics have inspired conventional calculational methods for perturbative quantum field theory to become more elegant and potentially more powerful methods. The material illustrates what may possibly be the most productive interface between mathematics and physics. As a result, it will be of interest to graduate students and researchers in theoretical and particle physics as well as mathematics.

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Summary

Up-to-date introduction to applications of knot theory and Feynman diagrams to quantum field theory.

Description

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 renormalization, 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 be of interest to theoretical and particle physicists, and mathematicians.

Critic Reviews

'... well structured and written.' Evelyn Weimar-Woods, Zentralblatt fur Mathematik 'This is a remarkable book of lecture notes that will fascinate theoretical physicists and pure mathematicians alike ... not only good reading ... recommended reading for anyone who wants to understand the subject properly.' The Mathematical Gazette 'In Knots and Feynman Diagrams, detective Dirk Kreimer recounts the unravelling of one of the great mysteries of modern physics.' Professor A. I. Solomon, Contemporary Physics