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  3. Knots and Feynman Diagrams
  • Cited by 34
      • Dirk Kreimer, Johannes Gutenberg Universität Mainz, Germany
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2010
      July 2000
      ISBN:
      9780511564024
      9780521587617
      DOI:
      https://doi.org/10.1017/CBO9780511564024
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.38kg, 272 Pages
      • Subjects:
      Mathematics, Physics and Astronomy, Mathematical Physics, Theoretical Physics and Mathematical Physics
      Series:
      Cambridge Lecture Notes in Physics (13)
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    • Selected: Digital
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    Subjects:
    Mathematics, Physics and Astronomy, Mathematical Physics, Theoretical Physics and Mathematical Physics
    Series:
    Cambridge Lecture Notes in Physics (13)
    Information

    Book 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.

    Reviews

    ‘… well structured and written.’

    Evelyn Weimar-Woods Source: Zentralblatt für 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.’

    Source: 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 Source: Contemporary Physics

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