Loops, Knots, Gauge Theories and Quantum Gravity

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Overview

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.

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Product Details

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.

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