# Split property for free massless finite helicity fields

June 13, 2018

We prove the split property for any finite helicity free quantum fields.
Finite helicity Poincar\'e representations extend to the conformal group and
the conformal covariance plays an essential role in the argument. The split
property is ensured by the trace class condition: Tr (exp(-s L_0)) is finite
for all s>0 where L_0 is the conformal Hamiltonian of the M\"obius covariant
restriction of the net on the time axis. We extend the argument for the scalar
case presented in [7]. 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 non-zero helicity.

Keywords:

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