Spinors in Four-Dimensional Spaces

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–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 (+ + + −) 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.