An Introduction To Twistor Theory

Evolving from graduate lectures given in London and Oxford, this introduction to twistor theory and modern geometrical approaches to space-time structure will provide graduate students with the basics of twistor theory, presupposing some knowledge of special relativity and differenttial geometry.

Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.

"Twistor theory is the remarkable mathematicl framework that was discovered by Roger Penrose in the course of research into gravitation and quantum theory. It has since developed into a broad many-faceted programme that attempts to resolve basic problems in physics by encoding the the structure of physical fields and indeed space-time itself into the complex analytical geometry of twistor space."--BOOK JACKET.

A text aimed at third year undergraduates and graduates in mathematics and physics, presenting elementary twistor theory as a universal technique for solving differential equations in applied mathematics and theoretical physics.

Geared toward students of physics and mathematics; presupposes no familiarity with twistor theory. "A huge amount of information, well organized and condensed into less than 200 pages." — Mathematical Reviews. 1989 edition.

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 1990 collection of review articles covers the considerable progress made in a wide range of applications of twistor theory.

Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.

Twistor theory is the remarkable mathematical framework that was discovered by Roger Penrose in the course of research into gravitation and quantum theory. It have since developed into a broad, many-faceted programme that attempts to resolve basic problems in physics by encoding the structure of physical fields and indeed space-time itself into the complex analytic geometry of twistor space. Twistor theory has important applications in diverse areas of mathematics and mathematical physics. These include powerful techniques for the solution of nonlinear equations, in particular the self-duality equations both for the Yang-Mills and the Einstein equations, new approaches to the representation theory of Lie groups, and the quasi-local definition of mass in general relativity, to name but a few. This volume and its companions comprise an abundance of new material, including an extensive collection of Twistor Newsletter articles written over a period of 15 years. These trace the development of the twistor programme and its applications over that period and offer an overview on the current status of various aspects of that programme. The articles have been written in an informal and easy-to-read style and have been arranged by the editors into chapter supplemented by detailed introductions, making each volume self-contained and accessible to graduate students and non-specialists from other fields. Volume II explores applications of flat twistor space to nonlinear problems. It contains articles on integrable or soluble nonlinear equations, conformal differential geometry, various aspects of general relativity, and the development of Penrose's quasi-local mass construction.