Loops, Knots, Gauge Theories and Quantum Gravity

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Rodolfo Gambini (Universidad de la República, Uruguay) Jorge Pullin (Pennsylvania State University)

Loops, Knots, Gauge Theories and Quantum Gravity

Rodolfo Gambini (Universidad de la República, Uruguay), Jorge Pullin (Pennsylvania State University), Abhay Ashtekar (Pennsylvania State University)

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English

Cambridge University Press
16 February 2023

Mathematics & Sciences; Gravity

Series: Cambridge Monographs on Mathematical Physics

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.

By: Rodolfo Gambini (Universidad de la República Uruguay), Jorge Pullin (Pennsylvania State University)
Foreword by: Abhay Ashtekar (Pennsylvania State University)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm, Spine: 18mm
Weight: 500g
ISBN: 9781009290166
ISBN 10: 1009290169
Series: Cambridge Monographs on Mathematical Physics
Pages: 340
Publication Date: 16 February 2023
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Format: Paperback
Publisher's Status: Active

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.