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Conformal quantum field theory and half-sided modular inclusions of von-Neumann-Algebras

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Abstract

LetN, ℳ be von-Neumann-Algebras on a Hilbert space ℋ, Ω a comon cyclic and separarting vector. Assume Ω to be cyclic and separating also forN ∩ ℳ. Denote byJ ℳ, J N the modular conjugations to (ℳ, Ω), Δℳ and Δ N the associated modular operators. If

and

these data define in a canonical way a conformal quantum field theory in a cricle. Conversely, the chiral part of a conformal quantum field theory in two dimensions always yields such data in a natural way.

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Authors and Affiliations

  1. Institut für Theoretische Physik, FU Berlin, D-14195, Berlin, Germany

    Hans-Werner Wiesbrock

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  1. Hans-Werner Wiesbrock
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Communicated by H. Araki

Partly supported by the DFG, SFB 288 Differentiageometrie und Quantenphysik

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Wiesbrock, HW. Conformal quantum field theory and half-sided modular inclusions of von-Neumann-Algebras. Commun.Math. Phys. 158, 537–543 (1993). https://doi.org/10.1007/BF02096802

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  • DOI: https://doi.org/10.1007/BF02096802

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