| Summary: | Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang<U+0013>Mills theory, are derived in detail using illustrative examples. Key topics and features: " Uniform treatment of the spinor formalism for four-dimensional spaces of any signature, not only the usual signature (+ + + <U+0012>) employed in relativity " Examples taken from Riemannian geometry and special or general relativity are discussed in detail, emphasizing the usefulness of the two-component spinor formalism " Exercises in each chapter " The relationship of Clifford algebras and Dirac four-component spinors is established " Applications of the two-component formalism, focusing mainly on general relativity, are presented in the context of actual computations Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tensor. This systematic and self-contained book is suitable as a seminar text, a reference book, and a self-study guide. Reviews from the author's previous book, 3-D Spinors, Spin-Weighted Functions and their Applications: In summary&the book gathers much of what can be done with 3-D spinors in an easy-to-read, self-contained form designed for applications that will supplement many available spinor treatments. The book&should be appealing to graduate students and researchers in relativity and mathematical physics. <U+0014>Mathematical Reviews The present book provides an easy-to-read and unconventional presentation of the spinor formalism for three-dimensional spaces with a definite or indefinite metric...Following a nice and descriptive introduction&the final chapter contains some applications of the formalism to general relativity. <U+0014>Monatshefte f<U+00fc>r Mathematik
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