It has been proposed that the appropriate global definition of a twistor, applicable to general curved vacuum space-times, would be as a charge for a massless field of helicity 3 I 2• In flat space-time, using the Dirac form of these potentials, these twistor charges arise as the “gauge freedom of the second kind” in a long exact sequence involving the first and second potentials for the field.

A construction due to Ward is recalled, in which potentials for massless fields can act as partial connections on non-linear bundles, integrable on 13-planes. This is generalized, in the case of helicity 3 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203734889/cc82ad37-66a9-4d5e-91f1-ce4dcbddbaf7/content/inequ642aa.tif"/> , to provide a full connection on a vector bundle of rank 3, leading to an expression whereby the usual Rarita-Schwinger potential is supplemented by a second potential.