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Title: The Theory of Spinors by Elie Cartan ISBN: 0-486-64070-1 Publisher: Dover Pubns Pub. Date: 01 February, 1981 Format: Paperback Volumes: 1 List Price(USD): $10.95 |
Average Customer Rating: 5 (2 reviews)
Rating: 5
Summary: Masterpiece based on the original lecture notes of Cartan
Comment: 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."
Rating: 5
Summary: Review of theory of spinors
Comment: 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.
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Title: Tensors, Differential Forms, and Variational Principles by David Lovelock, Hanno Rund ISBN: 0486658406 Publisher: Dover Publications Pub. Date: 01 April, 1989 List Price(USD): $15.95 |
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Title: Tensor Analysis on Manifolds by Richard L Bishop, Samuel I. Goldberg ISBN: 0486640396 Publisher: Dover Publications Pub. Date: 01 September, 1981 List Price(USD): $12.95 |
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Title: Differential Forms With Applications to the Physical Sciences by Harley Flanders ISBN: 0486661695 Publisher: Dover Publications Pub. Date: 01 January, 1990 List Price(USD): $11.95 |
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Title: Theory of Groups and Quantum Mechanics by H. Weyl ISBN: 0486602699 Publisher: Dover Publications Pub. Date: 01 October, 1984 List Price(USD): $16.95 |
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Title: Quantum Field Theory in a Nutshell by Anthony Zee ISBN: 0691010196 Publisher: Princeton University Press Pub. Date: 01 March, 2003 List Price(USD): $49.50 |
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