Twistor theory

Summary

Twistor theory is a programme proposed by Roger Penrose in 1967 that replaces spacetime points by objects in a complex space, twistor space. Points of complexified compactified Minkowski space correspond to lines in the complex projective space $\mathbb{CP}^3$. Light rays correspond to points of a real hypersurface of $\mathbb{CP}^3$. Under this correspondence, solutions of the massless field equations become holomorphic data on twistor space. Twistor methods are used in differential geometry, in integrable systems and in the computation of scattering amplitudes.