Split Property for Free Massless Finite Helicity Fields

We prove the split property for any finite helicity free quantum fields. Finite helicity Poincare representations extend to the conformal group C (cf.Mack in Commun Math Phys 55:1-28, 1977) and the conformal covariance plays an essential role in the argument: The split property is ensured by the trace class condition Trfor the conformal Hamiltonian L0 of the Mobius covariant restriction of the net on the time axis. We extend the argument for the scalar case presented in Buchholz et al. (Commun Math Phys 270:267-293, 2007). We provide the direct sum decomposition into irreducible representations of the conformal extension of any helicity-h representation to the subgroup of transformations fixing the time axis. Our analysis provides new relations among finite helicity representations and suggests a new construction for representations and free quantum fields with nonzero helicity.