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  • 9 - Loop representation: further developments

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 209-237
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  • 12 - Conclusions, present status and outlook

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 302-308
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  • References

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 309-318
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  • 6 - Lattice techniques

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 131-160
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  • 11 - The extended loop representation of quantum gravity

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 275-301
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  • Preface

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp xv-xvi
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  • 8 - The loop representation of quantum gravity

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 188-208
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  • 4 - Maxwell theory

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 88-112
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  • Dedication

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp vii-viii
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  • Contents

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp ix-xii
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  • Foreword

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp xiii-xiv
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  • 10 - Knot theory and physical states of quantum gravity

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 238-274
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  • 7 - Quantum gravity

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 161-187
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  • 1 - Holonomies and the group of loops

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 1-28
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  • 3 - The loop representation

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 52-87
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  • Index

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 319-324
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  • Frontmatter

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp i-vi
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  • 5 - Yang-Mills theories

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 113-130
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  • 2 - Loop coordinates and the extended group of loops

  • Rodolfo Gambini, Universidad de la República, Uruguay, Jorge Pullin, Pennsylvania State University
  • Foreword by Abhay Ashtekar, Pennsylvania State University
  • Book:
    Loops, Knots, Gauge Theories and Quantum Gravity
    Published online:
    10 November 2022
    Print publication:
    16 February 2023, pp 29-51
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Loops, Knots, Gauge Theories and Quantum Gravity
  • Rodolfo Gambini, Jorge Pullin
  • Foreword by Abhay Ashtekar
  • Published online:
    10 November 2022
    Print publication:
    16 February 2023
  • This volume provides a self-contained introduction to applications of loop representations, and the related topic of knot theory, in particle physics and quantum gravity. These topics are of considerable 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. The book begins with a detailed review of loop representation theory and then describes loop representations in Maxwell theory, Yang-Mills theories as well as lattice techniques. Applications in quantum gravity are then discussed, with the following chapters considering 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. First published in 1996, this title has been reissued as an Open Access publication on Cambridge Core.

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