Split property for free massless finite helicity fields

DOI10.1007/S00023-019-00820-4zbMATH Open1418.81057arXiv1806.04967OpenAlexW3100147193WikidataQ127622954 ScholiaQ127622954MaRDI QIDQ2001959

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Publication date: 11 July 2019

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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.

Full work available at URL: https://arxiv.org/abs/1806.04967

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