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From Spinors to Quantum Mechanics, by Gerrit Coddens
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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.
- Sales Rank: #1403938 in eBooks
- Published on: 2015-06-29
- Released on: 2015-09-10
- Format: Kindle eBook
From the Inside Flap
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.
Most helpful customer reviews
6 of 6 people found the following review helpful.
Wonderfully Insightful
By Jim Curry
I think that the spinor formalism is very important and will be central to important advances in the physics of the future. Certainly Penrose and Rindler's book is very good and beyond criticism by someone like me. However often I see the spinor formalism explained, I find it unsatisfactory. I end up wondering what it all really means, why it is as it is. Without a satisfactory intuition about the formalism, it is not possible for me to get decent results in my own research. It is the difference between reading the formal definition of a word in a dictionary and having an easy familiarity with its use in conversation. It is a small, but very important, difference. This book is not the standard presentation, and I suppose there may be some formalists in the audience who might not like it so much. For me, it gives very good and satisfactory explanations not just of the formalism but of its deeper meaning. It helps to form an intuition that would otherwise be achieved only after a very long time and with some frustration. This is a kinder and gentler way to get the question answered, "What does it really mean? What is it really all about?" Moving beyond the spinor formalism, the author discusses its substantial relation to quantum mechanics. While his conclusions may not gain universal acceptance immediately, it is a very, very useful step in getting more understanding of the quantum theory. It is a great testimony to the French system. It has the vigor and insight to support this kind of work. The French are great in mathematics at every generation. It is a testimony to the Imperial College Press that they would publish an unusual but insightful book. The author has, indeed, made this subject as simple as possible without over-simplification. I just love this book.
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