Canonical Gravity: From Classical to Quantum

1. Front Matter

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2. Prima facie questions in quantum gravity

   • C. J. Isham

   Pages 1-21

3. Hamilton's formalism for systems with constraints

   • A. Wipf

   Pages 22-58

4. The classical theory of canonical general relativity

   • R. Beig

   Pages 59-80

5. Ashtekar variables in classical general relativity

   • Domenico Giulini

   Pages 81-112

6. Quantization of systems with constraints

   • Petr Hájiček

   Pages 113-149

7. Canonical quantum gravity and the question of time

   • C. J. Isham

   Pages 150-169

8. The semiclassical approximation to quantum gravity

   • Claus Kiefer

   Pages 170-212

9. Loop representations

   • Bernd Brügmann

   Pages 213-253

10. Gauge theory and gravity in the loop formulation

    • Renate Loll

    Pages 254-288

11. Reduced models for quantum gravity

    • T. Thiemann

    Pages 289-318

12. Adjointness relations as a criterion for choosing an inner product

    • Alan D. Rendall

    Pages 319-326

13. Overview and outlook

    • Abhay Ashtekar

    Pages 327-367

14. Back Matter

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The search for a quantum gravity theory, a theory expected to combine the principles of general relativity and quantum theory, has led to some of the most deepest and most difficult conceptual and mathematical questions of modern physics. The present book, addressing these issues in the framework of recent versions of canonical quantization, is the first to present coherently the background for their understanding. Starting with an analysis of the structure of constrained systems and the problems of their quantization, it discusses the canonical formulation of classical relativity from different perspectives and leads to recent applications of canonical methods to create a quantum theory of gravity. The book aims to make accessible the most fundamental problems and to stimulate work in this field.

• Gravity
• general relativity
• quantum gravity
• quantum theory
• relativity

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