Twistors and induced representations of SU(2,2)

Abstract

We give an explicit realization of a series of representations of SU(2,2) induced by R+⊕SL(2,C). Vectors in these representation spaces are homogeneous spinor‐valued functions of two twistor variables. They may also be realized, in a frame‐dependent way, either as conformally invariant fields in Minkowski space or as homogeneous spinor‐valued functions on the O(2,4) null cone. The conformal invariance of the massless free fields is discussed from this point of view, and the twistor version of the field equations is derived. Finally, irreducible twistors are shown to correspond to conformally invariant fields satisfying the generalized twistor equation.