Invented by Dirac in creating his relativistic quantum theory of the electron, spinors are important in quantum theory, relativity, nuclear physics, atomic and molecular physics, and condensed matter physics. Essentially, they are the mathematical entities that correspond to electrons in the same way that ordinary wave functions correspond to classical particles. Because of their relations to the rotation group SO(n) and the unitary group SU(n), this discussion will be of interest to applied mathematicians as well as physicists.

Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.

In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.

This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in four-dimensional and three-dimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein–Dirac equations, nonlinear Heisenberg’s spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and post-graduate students of physical and mathematical specialties.

There is now a greater range of mathematics used in theoretical physics than ever. The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of differential geometry and Clifford algebras in classical field theory. Recent developments in particle physics have elevated the notion of spinor fields to considerable prominence, so that many new ideas require considerable knowledge of their properties and expertise in their manipulation. It is also widely appreciated now that differential geometry has an important role to play in unification schemes which include gravity. All the important prerequisite results of group theory, linear algebra, real and complex vector spaces are discussed. Spinors are approached from the viewpoint of Clifford algebras. This gives a systematic way of studying their properties in all dimensions and signatures. Importance is also placed on making contact with the traditional component oriented approach. The basic ideas of differential geometry are introduced emphasising tensor, rather than component, methods. Spinor fields are introduced naturally in the context of Clifford bundles. Spinor field equations on manifolds are introduced together with the global implications their solutions have on the underlying geometry. Many mathematical concepts are illustrated using field theoretical descriptions of the Maxwell, Dirac and Rarita-Schwinger equations, their symmetries and couplings to Einsteinian gravity. The core of the book contains material which is applicable to physics. After a discussion of the Newtonian dynamics of particles, the importance of Lorentzian geometry is motivated by Maxwell's theory of electromagnetism. A description of gravitation is motivated by Maxwell's theory of electromagnetism. A description of gravitation in terms of the curvature of a pseudo-Riemannian spacetime is used to incorporate gravitational interactions into the language of classical field theory. This book will be of great interest to postgraduate students in theoretical physics, and to mathematicians interested in applications of differential geometry in physics.

Marcellliesz's lectures delivered on October 1957 -January 1958 at the Uni versity of Maryland, College Park, have been previously published only infor mally as a manuscript entitled CLIFFORD NUMBERS AND SPINORS (Chap ters I - IV). As the title says, the lecture notes consist of four Chapters I, II, III and IV. However, in the preface of the lecture notes lliesz refers to Chapters V and VI which he could not finish. Chapter VI is mentioned on pages 1, 3, 16, 38 and 156, which makes it plausible that lliesz was well aware of what he was going to include in the final missing chapters. The present book makes lliesz's classic lecture notes generally available to a wider audience and tries somewhat to fill in one of the last missing chapters. This book also tries to evaluate lliesz's influence on the present research on Clifford algebras and draws special attention to lliesz's contributions in this field - often misunderstood.

This book on the theory of three-dimensional spinors and their applications fills an important gap in the literature. It gives an introductory treatment of spinors. From the reviews: "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