Book Description

Customer Reviews (3)

Masterpiece based on the original lecture notes of Cartan
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."

Review of theory of spinors
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 nullvector.Scalars, vectors and tensors are then described by theirproperties under simple geometrical transformations such as reflection androtation.The author then represents vectors as 2x2 matrices.Thetransformational properties of spinors are defined by their relation tovectors and tensors under these same simple transformations.The authorthen shows how spinors are useful for finding the irreduciblerepresentations of the rotation group.These concepts are then extended tohigher dimensional spinors.Specific applications are shown for Laplace'sequation, the Dirac equation and to general relativity.

The is anintroductory, inexpensive, brief and easy to read book.The book alsocovers a fair amount of ground.It is an excellent first book for thesubject.It does not contain modern developments in the field or someelements of the current notational system for representing spinors.Yet,for me it was the first book that gave me a sense of really understandingthe significance of the Dirac equation and quantum physic's concept ofspin.

Review of theory of spinors
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 nullvector.Scalars, vectors and tensors are then described by theirproperties under simple geometrical transformations such as reflection androtation.The author then represents vectors as 2x2 matrices.Thetransformational properties of spinors are defined by their relation tovectors and tensors under these same simple transformations.The authorthen shows how spinors are useful for finding the irreduciblerepresentations of the rotation group.These concepts are then extended tohigher dimensional spinors.Specific applications are shown for Laplace'sequation, the Dirac equation and to general relativity.

The is anintroductory, inexpensive, brief and easy to read book.The book alsocovers a fair amount of ground.It is an excellent first book for thesubject.It does not contain modern developments in the field or someelements of the current notational system for representing spinors.Yet,for me it was the first book that gave me a sense of really understandingthe significance of the Dirac equation and quantum physic's concept ofspin. ... Read more

Customer Reviews (1)

once overview, twice not suitable yet
As with all great masterpieces of math, I am not a critic for a good critique assumes expertise. I am an expert self-study beginner in pure and applied mathematics. My comments is for people in that disposition.
If you get a first look at the inside, then you quickly learn that the notation is very hard to understand for an introductory textbook. In addition, it is very dense and concise. Not much of an explanation to help first time beginners. It isn't meant to be introductory! I am sure that it is a standard classic for experts.
Elie Cartan was a truly great differential geometer! That is the reason I have the book; it's from a master.
In terms of approachability of the book, it is not that aproachable. If you are studying differential geometry, then it maybe right for you. I can say that I wanted an introductory self-study book and was disappointed.
It remains on the bookself and even got lost among other books for later review. When I have some more differential geometry courses or time I will try to decipher the notation. I can read math at the undergraduate level. This book is for sure for graduate students!
I just hope that in the future I can still make use of the book. I plan to go study differential geometry as a course with a professor. Then it would be nice to have something like this for reference work.
All in all, a masterpiece not easy to understand. It is how works of genius is. I better stick to reading math history books for introductions to math and self-studies. A better elementary book on Vector and Tensor Analysis is by Harry Lass which covers the fundamentals for elementary beginners like me. If you like Harry Lass's book then look forward to my other reviews. I am a struggling beginner that is not yet in graduate school for pure mathematics. Preparation is key and this book is an indication of what is ahead.
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Book Description
This book describes the life and achievements of the great Frenchmathematician, Elie Cartan. Here readers will find detaileddescriptions of Cartan's discoveries in Lie groups and algebras,associative algebras, differential equations, and differentialgeometry, as well of later developments stemming from his ideas.There is also a biographical sketch of Cartan's life. Amonumental tribute to a towering figure in the history ofmathematics, this book will appeal to mathematicians andhistorians alike. ... Read more

Product Description
From the series Actualities Scientifiques et Industrielles No 994. Exposes de Geometrie published under the direction of M.E. Cartan. 214 pages. Text in French. ... Read more