Twistor Geometry and Field Theory [Paperback]

This book deals with the twistor treatment of certain linear and non-linear partial differential equations in mathematical physics. The description in terms of twistors involves algebraic and differential geometry, and several complex variables, and results in a different kind of setting that gives a new perspective on the properties of space-time and field theories. The book is designed to be used by mathematicians and physicists and so the authors have made it reasonably self-contained. The first part contains a development of the necessary mathematical background. In the second part, Yang-Mills fields and gravitational fields (the basic fields of contemporary physics) are described at the classical level. In the final part, the mathematics and physics are married to solve a number of field-theoretical problems.Part I. Geometry: 1. Klein correspondence; 2. Fibre bundles; 3. Differential geometry; 4. Integral geometry; Part II. Field Theory: 5. Linear field theory; 6. Gauge theory; 7. General relativity; Part III. The Penrose Transform: 8. Massless free fields; 9. Self-dual gauge fields; 10. Self-dual space-times; 11. General gauge fields; 12. Stationary axisymmetric space-times; Special topics. ... skillfully written. It will serve as a relatively accessible introduction to twistor theory for many readers who have not studied the subject before. Others will find it useful as a refresher and as a source of many valuable insights. Nature