The volume provides an introduction to quantization in a broad context, and a systematic development of quantum geometry in Matrix Theory and string theory. It addresses advanced students and researchers in theoretical physics and mathematics, who are interested in quantum aspects of space-time and geometry in a physical context.
The volume provides an introduction to quantization in a broad context, and a systematic development of quantum geometry in Matrix Theory and string theory. It addresses advanced students and researchers in theoretical physics and mathematics, who are interested in quantum aspects of space-time and geometry in a physical context.
Harold Steinacker is senior scientist at the University of Vienna. He obtained his Ph.D. in physics at the University of California at Berkeley, and has held research positions at several universities. He has published more than 100 research papers, contributing significantly to the understanding of quantum geometry and matrix models in fundamental physics.
Inhaltsangabe
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.
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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