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Revision as of 15:46, 28 November 2023

Quantum Mechanics
Landau Quantum Mechanics.jpg
Information
Author Lev Landau
Language English
Series Course of Theoretical Physics
Publisher Butterworth Heinemann
Publication Date 1977
Pages 677
ISBN-13 978-0-7506-3539-8

Quantum Mechanics is mathematically simple compared to the previous two foundations of physics - classical mechanics and fields. It is linear, so no complicated manifolds like in mechanics or relativity. This is deceptive, but is a helpful crutch when first learning the subject. The true nature of quantum mechanics is geometric: the projective geometry of Hilbert space, geometric quantization from classical/symplectic geometry to quantum phase spaces, the moment map in symplectic geometry gives the map to the convex space of probability distributions, the bundles and connections appearing in the quantum Hall effect, and finally it is also a task to precisely interpret generalized functions, spectra of self-adjoint operators on function spaces, (projective) unitary group representations, and kernels/matrices of these general operators.

Applications

Ahlfors Complex Analysis Cover.jpg

Complex Analysis

Complex Analysis by Lars Ahlfors.

Woit Quantum Theory, Groups and Representations.png

Quantum Theory, Groups and Representations

Quantum Theory, Groups and Representations by Peter Woit

Fulton-Harris Representation Theory cover.jpg

Representation Theory

Representation Theory by William Fulton and Joe Harris.

Mackeyinducedquant cover.jpg

Induced Representations of Groups and Quantum Mechanics

Induced Representations of Groups and Quantum Mechanics by George Mackey.

Gelfand Generalized Functions vol 4 cover.png

Generalized Functions: Applications of Harmonic Analysis

Generalized Functions: Applications of Harmonic Analysis by Israel Gelfand and Naum Vilenkin.

Ahlforsriemann.jpg

Riemann Surfaces

Riemann Surfaces by Lars Ahlfors.

Lawson Spin Geometry cover.jpg

Spin Geometry

Spin Geometry by H. Blaine Lawson jr. and Marie-Louise Michelsohn.

Woodhouse Geometric Quantization cover.jpg

Geometric Quantization

Geometric Quantization by Nicholas Woodhouse.

Connes Noncommutative Geometry cover.jpg

Noncommutative Geometry

Noncommutative Geometry by Alain Connes.