Without using the customary Clifford algebras frequently studied in connection with therepresentations 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 YangMills 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 (+ + + ?) employed in relativity Examples taken from Riemannian geometry and special or general relativity arediscussed 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, arepresented in the context of actual computationsSpinors in Four-Dimensional Spaces is aimed at graduate students and researchers inmathematical 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.

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