An algebraic Haag's theorem

Abstract

Under natural conditions (such as split property and geometric modular action of wedge algebras) it is shown that the unitary equivalence class of the net of local (von Neumann) algebras in the vacuum sector associated to double cones with bases on a fixed space-like hyperplane completely determines an algebraic QFT model. More precisely, if for two models there is unitary connecting all of these algebras, then --- without assuming that this unitary also connects their respective vacuum states or spacetime symmetry representations --- it follows that the two models are equivalent. This result might be viewed as an algebraic version of the celebrated theorem of Rudolf Haag about problems regarding the so-called "interaction-picture" in QFT. Original motivation of the author for finding such an algebraic version came from conformal chiral QFT. Both the chiral case as well as a related conjecture about standard half-sided modular inclusions will be also discussed.

References in corpus (5)

• Multi-interval Subfactors and Modularity of Representations in Conformal Field Theory
• Extensions of Conformal Nets and Superselection Structures
• Extension of the structure theorem of Borchers and its application to half-sided modular inclusions
• On the uniqueness of diffeomorphism symmetry in Conformal Field Theory
• Conformal covariance and related properties of chiral QFT

Cited by in corpus (7)

• From vertex operator algebras to conformal nets and back
• Thermal States in Conformal QFT. II
• Thermal States in Conformal QFT. I
• Construction of two-dimensional quantum field models through Longo-Witten endomorphisms
• Braided categories of endomorphisms as invariants for local quantum field theories
• Spacelike deformations: Higher-helicity fields from scalar fields
• Massless Wigner particles in conformal field theory are free