Split property for free massless finite helicity fields
arXiv:1806.04967 · doi:10.1007/s00023-019-00820-4
Abstract
We prove the split property for any finite helicity free quantum fields. Finite helicity Poincaré 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 Möbius 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.
arXiv commentv2: Minor corrections, comments and references added, as to appear in Ann. H. Poinc
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Cited by in corpus (7)
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- The Bisognano-Wichmann property for asymptotically complete massless QFT
- Entanglement entropy of a Rarita-Schwinger field in a sphere
- Spacelike deformations: Higher-helicity fields from scalar fields
- Generalized symmetries and Noether's theorem in QFT