An Algebraic Jost-Schroer Theorem for Massive Theories

Abstract

We consider a purely massive local relativistic quantum theory specified by a family of von Neumann algebras indexed by the space-time regions. We assume that, affiliated with the algebras associated to wedge regions, there are operators which create only single particle states from the vacuum (so-called polarization-free generators) and are well-behaved under the space-time translations. Strengthening a result of Borchers, Buchholz and Schroer, we show that then the theory is unitarily equivalent to that of a free field for the corresponding particle type. We admit particles with any spin and localization of the charge in space-like cones, thereby covering the case of string-localized covariant quantum fields.

21 pages. The second (and crucial) hypothesis of the theorem has been relaxed and clarified, thanks to the stimulus of an anonymous referee. (The polarization-free generators associated with wedge regions, which always exist, are assumed to be temperate.)

References in corpus (4)

• Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
• Wedge-Local Quantum Fields and Noncommutative Minkowski Space
• Noncommutative Deformations of Wightman Quantum Field Theories
• Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories

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• The full electroweak interaction: an autonomous account
• Bound state operators and wedge-locality in integrable quantum field theories
• Massless Wigner particles in conformal field theory are free