U(n,n) AND GENERALIZED TWISTORS

Abstract

Publisher Summary Twistors have been introduced in relation to general relativity, conformal groups, and massless particles. The sympletic properties of twistor space have been used to obtain some irreducible representations of the Poincare group by Kostant–Souriau quantization. This chapter presents a pedagogical introduction to the twistor theory without use of dotted and undotted indices. The chapter further discusses the action of a poincare group on twistor space. There are three kinds of actions that are described in the chapter: action on the twistor space itself, action on the space of “twistors up to a phase,” and action on the twistor projective space. The chapter further describes the existence of six-dimensional orbits, which are canonical symplectic homogeneous spaces in the sense of the Kostant–Souriau theory when applied to the Poincare group. Each of them can be given the interpretation of phase space for a massless particle of helicity λ.