Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Conventions and notation
- 1 Modeling the early universe
- 2 Blowing up the universe: inflation
- 3 Observing perturbative quantum gravity: fluctuations
- 4 Quantizing gravity: canonical approach
- 5 Quantizing gravity: path integral approach
- 6 Linking gravity, quantum theory, and thermodynamics
- 7 Creating space and time: the no-boundary proposal
- 8 Interpreting the wave function
- 9 Transitioning to different spacetimes
- 10 Going deeper yet: stringy cosmology
- Appendix A Constants of nature and cosmological quantities
- Appendix B Picard{Lefschetz theory and saddle-point approximation
- Appendix C Useful functions
- Appendix D Solutions to exercises
- Appendix E Guide to the bibliography
- Bibliography
- Index
4 - Quantizing gravity: canonical approach
Published online by Cambridge University Press: 02 February 2026
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Conventions and notation
- 1 Modeling the early universe
- 2 Blowing up the universe: inflation
- 3 Observing perturbative quantum gravity: fluctuations
- 4 Quantizing gravity: canonical approach
- 5 Quantizing gravity: path integral approach
- 6 Linking gravity, quantum theory, and thermodynamics
- 7 Creating space and time: the no-boundary proposal
- 8 Interpreting the wave function
- 9 Transitioning to different spacetimes
- 10 Going deeper yet: stringy cosmology
- Appendix A Constants of nature and cosmological quantities
- Appendix B Picard{Lefschetz theory and saddle-point approximation
- Appendix C Useful functions
- Appendix D Solutions to exercises
- Appendix E Guide to the bibliography
- Bibliography
- Index
Summary
A variational principle for gravity, based on the Einstein–Hilbert action, is presented and augmented with a discussion of surface terms and boundary conditions. The ADM or Hamiltonian formalism is introduced, and gravity is rewritten in a (1+3)-dimensional decomposition. The theory is canonically quantized, which leads to the Wheeler–DeWitt equation. The properties of this equation are discussed, as well as those of JWKB semiclassical solutions. In this way it is shown how time is recovered in a semiclassical setting.
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- Quantum CosmologyAn Introduction, pp. 102 - 118Publisher: Cambridge University PressPrint publication year: 2026
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