Abstract
Existing results which show the zero rest mass field equations to be encoded in the geometry of projective twistor space are extended, and it is shown that the geometries of spaces of more than one twistor contain information concerning the scattering of such fields. Some general constructions which describe spacetime interactions in terms of cohomology groups on subvarieties in twistor space are obtained and are used to construct a purely twistorial description of spacetime propagators and of first order ϕ 4 {\phi ^4} scattering. Spacetime expressions concerning these processes are derived from their twistor counterparts, and a physical interpretation is given for the twistor constructions.
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