Split property for free massless finite helicity fields

TL;DR

This paper proves the split property for finite helicity free quantum fields, utilizing conformal symmetry and trace class conditions, and extends previous scalar case results to more general helicity representations.

Contribution

It establishes the split property for finite helicity fields using conformal covariance and extends the scalar case analysis to general helicity representations.

Findings

Split property holds for finite helicity free quantum fields.

Conformal covariance is crucial for the proof.

Provides a new construction approach for helicity representations.

Abstract

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.