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Knots and Feynman diagrams. (English) Zbl 0964.81052
Cambridge Lecture Notes in Physics. 13. Cambridge: Cambridge University Press. xii, 259 p. £21.95; $ 34.95/pbk (2000).
This book covers most recent developments which link perturbative quantum field theory via Feynman diagrams to the Hopf algebra structure of renormalization, knot theory, number theory and finally to noncommutative geometry. Each field is introduced by its basic concepts before the relations between them are worked out. The book is well structured and written in a fluent way which helps to digest the “heavy” content. It contains a long list of references.

81T18Feynman diagrams
81T15Perturbative methods of renormalization (quantum theory)
81-02Research monographs (quantum theory)
16W30Hopf algebras (assoc. rings and algebras) (MSC2000)
57M25Knots and links in the 3-sphere
11M99Analytic theory of zeta and L-functions
81R50Quantum groups and related algebraic methods in quantum theory
81R60Noncommutative geometry (quantum theory)
81T75Noncommutative geometry methods (quantum field theory)