Quantum Geometry, Matrix Theory, and Gravity

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. 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.

• | Author: Harold C. Steinacker
• | Publisher: Cambridge University Press
• | Publication Date: Apr 11, 2024
• | Number of Pages:
• | Language:
• | Binding: Hardback
• | ISBN-13: 9781009440783
• | ISBN-10: 1009440780