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Quantum geometry, matrix theory, and gravity

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quantum geometry, matrix theory, and gravityHarold C. Steinacker.
Author:	Steinacker, Harold C.
Published:	Cambridge, United Kingdom ; New York, NY :Cambridge University Press,2024.
Description:	xvi 402 p. :digital ;26 cm.
Notes:	Title from publisher's bibliographic system (viewed on 04 Apr 2024).
Subject:	Geometric quantization.
Online resource:	https://doi.org/10.1017/9781009440776
ISBN:	9781009440776$q(electronic bk.)

Quantum geometry, matrix theory, and gravity
Steinacker, Harold C.

Quantum geometry, matrix theory, and gravity[electronic resource] /Harold C. Steinacker. - Cambridge, United Kingdom ; New York, NY :Cambridge University Press,2024. - xvi 402 p. :digital ;26 cm.

Title from publisher's bibliographic system (viewed on 04 Apr 2024).

Differentiable manifolds -- Lie groups and coadjoint orbits -- Quantization of symplectic manifolds -- Quantum spaces and matrix geometry -- Covariant quantum spaces -- Noncommutative field theory -- Yang-Mills matrix models and quantum spaces -- Fuzzy extra dimensions -- Geometry and dynamics in Yang-Mills matrix models -- Higher-spin gauge theory on quantum spacetime -- Matrix theory : maximally supersymmetric matrix models -- Gravity as a quantum effect on quantum spacetime -- Matrix quantum mechanics and the BFSS model.

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.

ISBN: 9781009440776$q(electronic bk.)Subjects--Topical Terms:

230046
Geometric quantization.

LC Class. No.: QC174.17.G46 / S74 2024

Dewey Class. No.: 530.15

Quantum geometry, matrix theory, and gravity
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100 1 $a Steinacker, Harold C. $3 993956
245 1 0 $a Quantum geometry, matrix theory, and gravity $h [electronic resource] / $c Harold C. Steinacker.
260 $a Cambridge, United Kingdom ; New York, NY : $b Cambridge University Press, $c 2024.
300 $a xvi 402 p. : $b digital ; $c 26 cm.
500 $a Title from publisher's bibliographic system (viewed on 04 Apr 2024).
505 0 $a Differentiable manifolds -- Lie groups and coadjoint orbits -- Quantization of symplectic manifolds -- Quantum spaces and matrix geometry -- Covariant quantum spaces -- Noncommutative field theory -- Yang-Mills matrix models and quantum spaces -- Fuzzy extra dimensions -- Geometry and dynamics in Yang-Mills matrix models -- Higher-spin gauge theory on quantum spacetime -- Matrix theory : maximally supersymmetric matrix models -- Gravity as a quantum effect on quantum spacetime -- Matrix quantum mechanics and the BFSS model.
520 $a 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.
650 0 $a Geometric quantization. $3 230046
650 0 $a Gravity $x Mathematical models. $3 993957
650 0 $a String models. $3 251590
650 0 $a Matrices. $3 181876
856 4 0 $u https://doi.org/10.1017/9781009440776