Quantum Geometry, Matrix Theory, and Gravity (1版)

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【簡介】 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. 【目錄】 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.

Conversations on Quantum Gravity

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Conversations on Quantum Gravity ISBN13：9781107168879 出版社：Cambridge University Press 作者：Armas; Jacome (Jay) (Universiteit van Amsterdam) 裝訂／頁數：精裝／550頁 出版日：2021/08/31

Gravity: An Introduction to Einstein`s General Relativity (1版)

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書名：Gravity: An Introduction to Einstein`s General Relativity (PNIE) 作者：Hartle 出版社：Pearson 出版日期：2014/00/00 ISBN：9781292039145 內容簡介 ●Examples come first, derivations later. In this "physics first" approach, relevant simple solutions of the Einstein equation are presented first, before introducing the field equations of general relativity and their supporting mathematics. This brings the student to the heart of the physical phenomena as quickly as possible. ●The emphasis is on the exciting phenomena of gravitational physics and the growing connection between theory and observation. Global positioning system, black holes, X-ray sources, pulsars, quasars, gravitational waves, the big bang, and the large scale structure of the universe, for example, are used to illustrate the widespread role of how general relativity describes a wealth of everyday and exotic phenomena. ●Novel and simple examples are presented to keep the presentation concise and accessible: for instance, Schwarzschild black hole, spherical stars, weak gravitational waves in flat spacetime. ●Mathematics, beyond the typical advanced calculus knowledge, is kept to a minimum. Only absolutely essential new mathematical concepts are introduced, and these only when needed. ●The text's layered structure allows the text to be used for a range of courses depending on the length and level of the course—from junior level to introductory graduate level in physics and astronomy. After just the first few chapters, a student will take away a broad introduction to some of the basic phenomena of gravitational physics, and not just mathematical tools. ●Illustrative boxes are interspersed throughout, providing students with applications, experiments, ideas, examples, and interesting sidelights that extend and complement concepts presented in the basic text without interrupting its flow. 目錄 I. SPACE AND TIME IN NEWTONIAN PHYSICS AND SPECIAL RELATIVITY. 1. Gravitational Physics. 2. Geometry as Physics. 3. Space, Time, and Gravity in Newtonian Physics. 4. Principles of Special Relativity. 5. Special Relativistic Mechanics. II. THE CURVED SPACETIMES OF GENERAL RELATIVITY. 6. Gravity as Geometry. 7. The Description of Curved Spacetime. 8. Geodesics. 9. The Geometry Outside a Spherical Star. 10. Solar System Tests of General Relativity. 11. Relativistic Gravity in Action. 12. Gravitational Collapse and Black Holes. 13. Astrophysical Black Holes. 14. A Little Rotation. 15. Rotating Black Holes. 16. Gravitational Waves. 17. The Universe Observed. 18. Cosmological Models. 19. Which Universe and Why? III. THE EINSTEIN EQUATION. 20. A Little More Math. 21. Curvature and the Einstein Equation. 22. The Source of Curvature. 23. Gravitational Wave Emission. 24. Relativistic Stars.