Twistors and Fields With Sources on Worldlines

It is shown that zero-rest-mass fields with sources on an analytic worldline are naturally defined on a double cover of some region of Minkowski space. Twistor spaces are constructed that correspond to such regions and these turn out to be non-Hausdorff spaces, obtained by identifying two copies of regions in ordinary twistor space, except on a ruled surface that corresponds to the worldline. It is shown that cohomology classes on the twistor space corresponds to sourced fields on Minkowski space, thus extending the twistor description of massless fields.