Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Mathematical background
- Part II Quantum spaces and geometry
- 3 Quantization of symplectic manifolds
- 4 Quantum spaces and matrix geometry
- 5 Covariant quantum spaces
- Part III Noncommutative field theory and matrix models
- Part IV Matrix theory and gravity
- Appendix A Gaussian integrals over matrix spaces
- Appendix B Some SO(D) group theory
- Appendix C Torsion identities
- Appendix D Some integrals
- Appendix E Functions on coadjoint orbits
- Appendix F Glossary and notations
- References and Further Reading
- Index
3 - Quantization of symplectic manifolds
from Part II - Quantum spaces and geometry
Published online by Cambridge University Press: 04 April 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Mathematical background
- Part II Quantum spaces and geometry
- 3 Quantization of symplectic manifolds
- 4 Quantum spaces and matrix geometry
- 5 Covariant quantum spaces
- Part III Noncommutative field theory and matrix models
- Part IV Matrix theory and gravity
- Appendix A Gaussian integrals over matrix spaces
- Appendix B Some SO(D) group theory
- Appendix C Torsion identities
- Appendix D Some integrals
- Appendix E Functions on coadjoint orbits
- Appendix F Glossary and notations
- References and Further Reading
- Index
Summary
The general concept of quantization is discussed, which provides the starting point for the further developments in this book. Starting with the concepts familiar from quantum mechanics, a number of quantum spaces defined via explicit operators on Hilbert space are discussed in detail, including compact and non-compact examples.
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- Quantum Geometry, Matrix Theory, and Gravity , pp. 31 - 75Publisher: Cambridge University PressPrint publication year: 2024