## About this book

### Introduction

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.

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.*

**—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.*

**—Monatshefte für Mathematik**

### Keywords

Conformal Curvature Curvature Spinors Dirac Spinors Einstein’s Equations Killing Bispinors Potential Riemannian geometry Self-Dual Yang–Mills Fields Spinor Algebra Theoretical physics Vector space algebra manifold

#### Authors and affiliations

- Gerardo F. Torres del Castillo

- 1.Universidad Autónoma de PueblaInstituto de CienciasPueblaMexico

### Bibliographic information