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This book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which spinors behave. The book concentrates on the algebra and calculus of spinors connected with curved space-time. Many of the well-known tensor fields in general relativity are shown to have spinor counterparts. An analysis of the Lanczos spinor concludes the book, and some of the techniques so far encountered are applied to this. Exercises play an important role throughout and are given at the end of each chapter.

General relativity (Physics) --- Spinor analysis. --- Calculus of spinors --- Spinor calculus --- Spinors, Theory of --- Algebra --- Wave mechanics --- Calculus of tensors --- Vector analysis --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics)

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This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.

Spinor analysis. --- Space and time. --- Geometry, Differential. --- Mathematical physics. --- Physical mathematics --- Physics --- Differential geometry --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Hyperspace --- Relativity (Physics) --- Calculus of spinors --- Spinor calculus --- Spinors, Theory of --- Algebra --- Wave mechanics --- Calculus of tensors --- Vector analysis --- Mathematics

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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.

Mathematics. --- Physics. --- Spinor analysis. --- Spinor analysis --- Mathematics --- Engineering & Applied Sciences --- Applied Physics --- Algebra --- Calculus --- Physical Sciences & Mathematics --- Calculus of spinors --- Spinor calculus --- Spinors, Theory of --- Topological groups. --- Lie groups. --- Applied mathematics. --- Engineering mathematics. --- Gravitation. --- Topological Groups, Lie Groups. --- Mathematical Methods in Physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Applications of Mathematics. --- Wave mechanics --- Calculus of tensors --- Vector analysis --- Topological Groups. --- Mathematical physics. --- Math --- Science --- Physical mathematics --- Physics --- Groups, Topological --- Continuous groups --- Engineering --- Engineering analysis --- Mathematical analysis --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Properties