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.

‘… 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 Source: Mathematical Reviews

‘This book … very well-written and fairly complete, is definitely advanced … it’s quite a ride for the stout of heart.’

Kevin Gillette Source: Words Across Time