Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities. Covers generalities on the group of rotations in n-dimensional space, the theory of spinors in spaces of any number of dimensions and much more.
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41 of 42 people found the following review helpful:
5.0 out of 5 stars
Review of theory of spinors,
By Reader "Reader" (GA, USA) - See all my reviews
This review is from: The Theory of Spinors (Dover Books on Mathematics) (Paperback)
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.
10 of 11 people found the following review helpful:
5.0 out of 5 stars
Review of theory of spinors,
By Reader "Reader" (GA, USA) - See all my reviews
This review is from: The Theory of Spinors (Dover Books on Mathematics) (Paperback)
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.
7 of 7 people found the following review helpful:
4.0 out of 5 stars
translated from French,
By R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews (VINE VOICE) (REAL NAME)
This review is from: The Theory of Spinors (Dover Books on Mathematics) (Paperback)
We have Weyl, Pauli, Dirac and Cartan to thank for our modern
theory of groups in physics. This book published in 1937 has none of the later Lie algebra representations of the Cartan generalization of groups and thus, like Weyl's similar book may deceive the reader into thinking he understands when he has only a rough and not very even introduction to these groups. This book doesn't reach much higher than SU(2), SO(3) and the Dirac U(1)*SU(2)*SU(2). The standard model of physics deals with the symmetry breaking of SU(5) ( the Cartan A_4 group) to U(1)*SU(2)*SU(3). The Lie algebras and irreducible Cartan representations of such higher symmetries will demand the student read further than this text. So this book is an historical introduction that gives the starting basis for the mathematics needed by modern students in physics and chemistry.
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