On the twistor description of massive fields

This paper forms a part of the twistor programme whereby constructions of physics on Minkowski space are transferred, it is hoped, to simpler constructions on Penrose’s twistor-space . We show how the Penrose transform may be used to describe solutions of the Dirac equations on Minkowski space in terms of certain cohomology classes on a related five-dimensional complex manifold. This is accomplished along the same lines as the corresponding representation of massless fields. It means that Penrose’s integral formulae for massive fields may be interpreted cohomologically. We also give a brief discussion of the spin operator in twistor space.