Theory of Spinors

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Summary: Masterpiece based on the original lecture notes of Cartan
Review: This book is a great work on the subject of spinors. Since it is based solely on Elie Cartan's work, the termonology and wording reflects that of the transition coming out of the Post-Victorian math era (i.e., when quaternions and the more abstract mathematics where used for applied calculations in physics, which have been replaced with scalars and vectors). The geometrical definition layed down in the third chapter makes this a very comprehensive book for the newcomer to the subject. Quote page 42., "A spinor is thus a sort of "directed" or "polarized" isotropic vector; a rotation about an axis through an angle of 2pi changes the polarization of this isotropic vector."

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Summary: Looking to link Quantum Mechanics with Group Theory?
Review: This book is extremely easy to understand compared to other texts on the subject. It serves well to lead you to other books such as Hermann Weyl's text on Quantum Groups. The author has the most intuitive explanations that I have seen in any other works on the subject. This is extremely useful for me, since I was trained as an electrical engineer, and sometimes I feel that authors of mathematics text get lost in formal definitions in n space; although important I feel that relating them to basic understandable behavior in 3-space is especially useful, and done well in this text. It is my current thought that formulating a certain level of abstraction is necessary for the furthering of mathematics, like what is done with Geometric Algebra, but making these relations clear for myself at least in the physical world has been an important hard earned step. I believe this book to be simply outstanding and recommend it to anyone interested in linking group theory to Quantum Mechanics, especially Engineers who don't want to physically build anything but like math, like myself. On the subject, I used this book to understand the mathematics in the majority of texts on Quantum Mechanics, I approach the equations now, not as an abstract concepts but looking at their space behavior even for n space; Hopefully I will be able to exploit some useful properties of the lie group useful for Quantum Computation. This book is one of my current favorites; I recommend it, but especially to those interested in Quantum Mechanics or Group Theory from a non Mathematics background. Of course this is not a beginning text, but it can be used along side a beginning text such as "Algebraic Structures" or "A course on Group Theory" both from Dover. I have never taken a class on Group Theory but with these texts and about 5 others on Topology and some other subjects along with several on Quantum Computing (my application for leaning group theory) I was able to teach myself what I needed; but group theory is covered in other places, they just don't call it that. This book was the most helpful, the best written and the most intuitive. A classic... The only thing bad about it is that more things have happened in the subject since it was published, but this covers the main points, and is where you may want to start.

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Summary: Review of theory of spinors
Review: This is an excellent introductory book on spinors, the basic mathematical object used to represent particles with spin.

The author begins by defining the spinor as a form of a square root of a 3 dimensional null vector. Scalars, vectors and tensors are then described by their properties under simple geometrical transformations such as reflection and rotation. The author then represents vectors as 2x2 matrices. The transformational properties of spinors are defined by their relation to vectors and tensors under these same simple transformations. The author then shows how spinors are useful for finding the irreducible representations of the rotation group. These concepts are then extended to higher dimensional spinors. Specific applications are shown for Laplace's equation, the Dirac equation and to general relativity.

The is an introductory, inexpensive, brief and easy to read book. The book also covers a fair amount of ground. It is an excellent first book for the subject. It does not contain modern developments in the field or some elements of the current notational system for representing spinors. Yet, for me it was the first book that gave me a sense of really understanding the significance of the Dirac equation and quantum physic's concept of spin.