An Introduction to Twistor Theory

This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level.

S. A. Huggett (Author), K. P. Tod (Author)

9780521456890, Cambridge University Press

Paperback, published 21 July 1994

192 pages
23 x 15.7 x 2 cm, 0.394 kg

'In all, the book provides a pleasant starting point for the study of this fascinating subject.' Dr F. E. Burstall, Contemporary Physics

This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. The choice of material presented has evolved from graduate lectures given in London and Oxford and the authors have aimed to retain the informal tone of those lectures. The book will provide graduate students with an introduction to the literature of twistor theory, presupposing some knowledge of special relativity and differential geometry. It would also be of use for a short course on space-time structure independently of twistor theory. The physicist could be introduced gently to some of the mathematics which has proved useful in these areas, and the mathematician could be shown where sheaf cohomology and complex manifold theory can be used in physics.

1. Introduction
2. Review of tensor algebra
3. Lorentzian spinors at a point
4. Spinor fields
5. Compactified Minkowski space
6. The geometry of null congruences
7. The geometry of twistor space
8. Solving the zero rest mass equations I
9. Sheaf cohomology
10. Solving the zero rest mass equations II
11. The twisted photon and Yang–Mills constructions
12. The non-linear graviton
13. Penrose's quasi-local momentum
14. Cohomological functionals
15. Further developments and conclusion
Appendix: The GHP equations.

Subject Areas: Differential & Riemannian geometry [PBMP]