Book contents
- Frontmatter
- Contents
- Foreword
- Preface
- 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 gravity
- 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
Preface
- Frontmatter
- Contents
- Foreword
- Preface
- 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 gravity
- 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
Summary
Loops have been used as a tool to study classical and quantum Yang–Mills theory since the work of Mandelstam in the early 1960s. They have led to many insights concerning the non-perturbative dynamics of the theory including the issue of confinement and the lattice formulation. Since the inception of the Asthekar new variables, loop techniques have also found important applications in quantum gravity. Due to the diffeomorphism invariance of the theory they have led to surprising connections with knot theory and topological field theories.
The intention in this book is to present several of these results in a common framework and language. In particular it is an attempt to combine ideas developed some time ago in the context of Yang–Mills theories with the recent applications in quantum gravity. It should be emphasized that our treatment of Yang–Mills theories only covers a small part of all results obtained with loops: that which seems of most relevance for applications in gravity.
This book should allow people from outside the field to gain access in a pedagogical way to the current state of the art. Moreover, it allows experts within this wide field with heterogeneous backgrounds to learn about specific results outside their main area of expertise and as a reference volume. It should be well suited as an introductory guide for graduate students who want to get started in the subject.
- Type
- Chapter
- Information
- Loops, Knots, Gauge Theories and Quantum Gravity , pp. xv - xviPublisher: Cambridge University PressPrint publication year: 1996