The Bisognano-Wichmann property on nets of standard subspaces, some sufficient conditions

Abstract

We discuss the Bisognano-Wichmann property for local Poincaré covariant nets of standard subspaces. We give a sufficient algebraic condition on the covariant representation ensuring the Bisognano-Wichmann and Duality properties without further assumptions on the net called modularity condition. It holds for direct integrals of scalar massive and massless representations. We present a class of massive modular covariant nets not satisfying the Bisognano-Wichmann property. Furthermore, we give an outlook in the standard subspace setting on the relation between the Bisognano-Wichmann property and the Split property.

Final version. To appear in Annales Henri Poincaré

References in corpus (5)

• An Algebraic Construction of Boundary Quantum Field Theory
• Where Infinite Spin Particles Are Localizable
• Nuclearity and Thermal States in Conformal Field Theory
• Localization in Nets of Standard Spaces
• Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases

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