Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Mathematical background
- Part II Quantum spaces and geometry
- Part III Noncommutative field theory and matrix models
- 6 Noncommutative field theory
- 7 Yang–Mills matrix models and quantum spaces
- 8 Fuzzy extra dimensions
- 9 Geometry and dynamics in Yang–Mills matrix models
- 10 Higher-spin gauge theory on quantum spacetime
- 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
7 - Yang–Mills matrix models and quantum spaces
from Part III - Noncommutative field theory and matrix models
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
- Part III Noncommutative field theory and matrix models
- 6 Noncommutative field theory
- 7 Yang–Mills matrix models and quantum spaces
- 8 Fuzzy extra dimensions
- 9 Geometry and dynamics in Yang–Mills matrix models
- 10 Higher-spin gauge theory on quantum spacetime
- 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
This chapter discusses the central models of interest, dubbed Yang–Mills matrix models. We explain how quantum spaces are obtained as nontrivial backgrounds or vacua of these models. Their quantization is discussed, both from a perturbative as well as a nonperturbative point of view.
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- Quantum Geometry, Matrix Theory, and Gravity , pp. 223 - 251Publisher: Cambridge University PressPrint publication year: 2024