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Loops, Knots, Gauge Theories and Quantum Gravity

Loops, Knots, Gauge Theories and Quantum Gravity

$76.00

Part of Cambridge Monographs on Mathematical Physics

  • Date Published: July 2000
  • availability: Available
  • format: Paperback
  • isbn: 9780521654753

$76.00
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About the Authors
  • Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. This text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. The book begins with a detailed review of loop representation theory. It then goes on to describe loop representations in Maxwell theory, Yang-Mills theories, as well as lattice techniques. The authors then discuss applications in quantum gravity in detail. Following chapters consider knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research.

    • It casts several topics from different areas of physics in a common language and a single perspective
    • The book is self-contained from the point of view of a graduate student who wants to get started in the field
    • It introduces several notions of sophisticated mathematics that are needed to discuss the physics in a simple fashion
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    Reviews & endorsements

    "...the book is useful for an immersion in the subject, researchers working in the field, no doubt, will find it pleasant because of the precise natural style of the authors, who are pioneers and leaders in the field." Hugo A. Morales, Mathematical Reviews

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    Product details

    • Date Published: July 2000
    • format: Paperback
    • isbn: 9780521654753
    • length: 340 pages
    • dimensions: 235 x 191 x 18 mm
    • weight: 0.59kg
    • contains: 33 b/w illus.
    • availability: Available
  • Table of Contents

    1. Holonomies and the group of loops
    2. Loop coordinates and the extended group of loops
    3. The loop representation
    4. Maxwell theory
    5. Yang-Mills theories
    6. Lattice techniques
    7. Quantum gravity
    8. The loop representation of quantum theory
    9. Loop representation: further developments
    10. Knot theory and physical states of quantum gravity
    11. The extended loop representation of quantum gravity
    12. Conclusions: present status and outlook
    References
    Index.

  • Authors

    Rodolfo Gambini, Universidad de la República, Uruguay

    Jorge Pullin, Pennsylvania State University

    Foreword

    Abhay Ashtekar

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