# Loops, Knots, Gauge Theories (Cambridge Monographs on Mathematical Physics)

Cambridge University Press

Edition: New Ed, 8/21/2008

EAN 9780521654753, ISBN10: 0521654750

Paperback, 340 pages, 23.5 x 19 x 2 cm

Language: English

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.

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.