Introduction

Summary

In 1967 Roger Penrose introduced the notion of twistors and twistor geometry in a seminal paper entitled ‘Twistor Algebra’. Since that time, there has developed a significant literature and research movement in many parts of the world, devoted to understanding the ramifications of his original proposals. The fundamental thesis of the ‘twistor program’ is to replace the usual background space-time, in which most of the phenomena of modern physics is presented, by a new background space of twistors. In particular, the physical phenomena and the equations describing them are to be reinterpreted in this new background space, with the intent of gaining new insight into them. There is some analogy to introducing ‘momentum space’ and using the Fourier transform to transform back and forth from space-time to momentum space. A principal aim of this book is to present a systematic study of the main developments in the applications of twistor geometry to problems arising from theoretical physics.

There are several aspects to the twistor program. First, it has been quite successful in giving new insight into various nonlinear classical field equations which are of interest to the physics community, as well as a new point of view for the much better understood classical linear field theories.