twistor

A twistor is a mathematical object that can be used to reformulate problems in theoretical physics, particularly in general relativity and quantum field theory. The concept was introduced by Roger Penrose in the early 1970s. Twistors provide a geometric way to describe points in spacetime and fields on spacetime. Instead of dealing with points in Minkowski spacetime, which are represented by vectors, twistors represent a more fundamental, algebraic entity. This algebraic entity can be thought of as encoding information about a point and a direction, or a null line in spacetime.

The space of all twistors is called twistor space. Twistor theory aims to express physical laws and concepts in terms of twistor geometry. One of the key ideas is that fields in spacetime can be seen as holomorphic functions on certain complex manifolds related to twistor space. This approach has led to new insights and alternative derivations of known results in physics. For example, the scattering amplitudes in certain quantum field theories can be elegantly expressed using twistor methods. The connection between spacetime and twistor space is typically established through a mapping that takes points in spacetime to specific subspaces in twistor space. This correspondence is crucial for translating physical problems into the language of twistors and then back again.