The Twistor Particle Programme

Classification schemes for elementary particles are discussed using methods of twistor theory, with particular emphasis on the relationship of twistor theory to the Weinberg-Salam model and the Georgi-Glashow SU(5) model. Particle states correspond, in this picture, to holomorphic functions of several twistors. Observables are defined in erms of holomorphic differential operators which act on these functions. For the Weinberg-Salam model holomorphic functions of three twistors are considered. A specific proposal is made for the incorporation of muons and heavy leptons into the model, so that these particles can also be described using functions of three twistors. Holomorphic functions of six twistors are used to build up the states of the Georgi-Glashow model-five of the twistors transform as a quintet under SU(5), whereas the sixth twistor transforms as an SU(5) singlet. The model incoporates an infinite set of fermion generations, all of which have the same SU(5) multiplet structure.