Knots and Feynman Diagrams
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.
- Author is leading pioneer in this field of research
- Self-contained and provides pedagogical coverage of recent developments previously only discussed in journals
- Includes many helpful diagrams
Reviews & endorsements
This is a fascinating story of the search for a conjecture." Mathematical Reviews
Product details
July 2000Paperback
9780521587617
272 pages
229 × 154 × 17 mm
0.38kg
97 b/w illus. 8 tables
Out of stock in print form with no current plan to reprint
Table of Contents
- 1. Introduction
- 2. Perturbative quantum field theory
- 3. The Hopf algebra structure of renormalization
- 4. Rationality: no knots, no transcendentals
- 5. The simplest link diagrams
- 6. Necessary topics from knot theory
- 7. Knots to numbers
- 8. One-loop words
- 9. Euler-Zagier sums
- 10. Knots and transcendentals
- 11. The 4-term relation
- 12. Hopf algebras, non-commutative geometry, and what else?