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Zbl 0964.81052
Kreimer, Dirk
Knots and Feynman diagrams. (English)
[B] Cambridge Lecture Notes in Physics. 13. Cambridge: Cambridge University Press. xii, 259 p. \sterling 21.95; \$ 34.95/pbk (2000). ISBN 0-521-58761-1

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.
[Evelyn Weimar-Woods (Berlin)]

MSC 2000:: *81T18 Feynman diagrams
81T15 Perturbative methods of renormalization
81-02 Research monographs (quantum theory)
16W30 Hopf algebras (assoc. rings and algebras)
57M25 Knots and links in the 3-sphere
11M99 Analytic theory of zeta and L-functions
81R50 Quantum groups and related algebraic methods in quantum theory
81R60 Noncommutative geometry
81T75 Noncommutative geometry methods

Keywords: perturbative quantum field theory; number theory; noncommutative geometry

Cited in: Zbl 1137.81017 Zbl 1101.57012

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