We prove the split property for any finite helicity free quantum fields. Finite helicity Poincaré 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 Tr(e-βL0)<∞ for the conformal Hamiltonian L of the Möbius 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.

Split Property for Free Massless Finite Helicity Fields / Longo, R.; Morinelli, V.; Preta, F.; Rehren, K. -H.. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - 20:8(2019), pp. 2555-2584. [10.1007/s00023-019-00820-4]

Split Property for Free Massless Finite Helicity Fields

Morinelli V.;
2019

Abstract

We prove the split property for any finite helicity free quantum fields. Finite helicity Poincaré 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 Tr(e-βL0)<∞ for the conformal Hamiltonian L of the Möbius 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1584738
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