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Coddens G. From Spinors to Quantum Mechanics

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Coddens G. From Spinors to Quantum Mechanics
Imperial College Press, UK, USA, 2015. — 404 p. — ISBN 1783266368.
From Spinors to Quantum Mechanics discusses group theory and its use in quantum mechanics. Chapters 1 to 4 offer an introduction to group theory, and it provides the reader with an exact and clear intuition of what a spinor is, showing that spinors are just a mathematically complete notation for group elements. Chapter 5 contains the first rigorous derivation of the Dirac equation from a simple set of assumptions. The remaining chapters will interest the advanced reader who is interested in the meaning of quantum mechanics. They propose a novel approach to the foundations of quantum mechanics, based on the idea that the meaning of the formalism is already provided by the mathematics.
In the traditional approach to quantum mechanics as initiated by Heisenberg, one has to start from a number of experimental results and then derive a set of rules and calculations that reproduce the observed experimental results. In such an inductive approach the underlying assumptions are not given at the outset. The reader has to figure them out, and this has proven to be difficult. The book shows that a different, bottom-up approach to quantum mechanics is possible, which merits further investigation as it demonstrates that with the methods used, the reader can obtain the correct results in a context where one would hitherto not expect this to be possible.
Readership: Graduate students and researchers in the field of quantum mechanics.
Contents
Introduction
Introduction to Groups
Spinors in the Rotation Group
Spinors in the Homogeneous Lorentz Group
The Dirac Equation from Scratch
Towards a Better Understanding of Quantum Mechanics
The Hidden-Variables Issue and the Bell Inequalities
Equivalence of the Bohr-Sommerfeld and Dirac Theories for the Hydrogen Atom
The Problem of the Electron Spin within a Magnetic Field
The Double-Slit Experiment and the Superposition Principle
A Caveat About the Limitations of Group Theory
Spin and Angular Momentum as Vector and Bi-Vector Concepts
Appendixes
Discovering SL(2,C) Starting from the Cartan Representation
Differences in the Spinor Formalisms Between SO(3) and SL(2,C)
Additional Results on the Lorentz Group
The Analogy Between Electromagnetism and Gravitation
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