Lops, Knots, Gauge Theories and Quantum Gravity (Broché)

Jorge Pullin, Rodolfo Gambini

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  • Cambridge University Press

  • Paru le : 26/05/2000
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Now in paperback, this text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. 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 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. Applications in quantum gravity are then discussed in detail. Following chapters move on to 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. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.
    • Holonomies and the group of loops
    • Loop coordinates and the extended group of loops
    • The loop representation
    • Maxwell theory
    • Yang-Mills theories
    • Lattice techniques
    • Quantum gravity
    • The loop representation of quantum gravity
    • Loop representation: further developments
    • Knot theory and physical states of quantum gravity
    • The extended loop representation of quantum gravity
    • Conclusions, present status and outlook.

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