By reformulating conformal invariance in terms of differential operators acting directly on helicity states, we are able to establish the restrictions placed by this invariance on the helicity amplitudes for the scattering of four particles of arbitrary spin. The result is helicity conservation in the form ${\lambda }_1+{\lambda }_2={\lambda }_3+{\lambda }_4$ except for exceptional amplitudes $T_{\lambda ,\lambda ;-\lambda ,-\lambda }$, which survive (subject, however, to a differential constraint). It is conjectured that traces of these restrictions will survive in hadron physics at fixed angle and high energy if indeed the underlying dynamics is asymptotically free.

• Received 26 December 1973

DOI:https://doi.org/10.1103/PhysRevD.10.1321