Quantum Geometry, Matrix Theory, and Gravity
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Quantum Geometry, Matrix Theory, and Gravity

Quantum Geometry, Matrix Theory, and Gravity

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International Edition


About the Book

Building on mathematical structures familiar from quantum mechanics, this book provides an introduction to quantization in a broad context before developing a framework for quantum geometry in Matrix Theory and string theory. Taking a physics-oriented approach to quantum geometry, this framework helps explain the physics of Yang–Mills-type matrix models, leading to a quantum theory of space-time and matter. This novel framework is then applied to Matrix Theory, which is defined through distinguished maximally supersymmetric matrix models related to string theory. A mechanism for gravity is discussed in depth, which emerges as a quantum effect on quantum space-time within Matrix Theory. Using explicit examples and exercises, readers will develop a physical intuition for the mathematical concepts and mechanisms. It will benefit advanced students and researchers in theoretical and mathematical physics, and is a useful resource for physicists and mathematicians interested in the geometrical aspects of quantization in a broader context.

Table of Contents:
Preface; The trouble with spacetime; Quantum geometry and Matrix theory; Part I. Mathematical Background: 1. Differentiable manifolds; 2. Lie groups and coadjoint orbits; 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: 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: 11. Matrix theory: maximally supersymmetric matrix models; 12. Gravity as a quantum effect on quantum spacetime; 13. Matrix quantum mechanics and the BFSS model; Appendixes; References; Index.


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Product Details
  • ISBN-13: 9781009440783
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Height: 261 mm
  • No of Pages: 420
  • Returnable: N
  • Spine Width: 28 mm
  • Width: 185 mm
  • ISBN-10: 1009440780
  • Publisher Date: 11 Apr 2024
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Returnable: N
  • Weight: 1004 gr


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