Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions | Zendy

Klaus Fredenhagen | Zendy; Martin Jörß | Zendy

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Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions

Author(s) -

Klaus Fredenhagen,

Martin Jörß

Publication year - 1996

Publication title -

communications in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.662

H-Index - 152

eISSN - 1432-0916

pISSN - 0010-3616

DOI - 10.1007/bf02099249

Subject(s) - operator product expansion , conformal field theory , minkowski space , conformal map , product (mathematics) , primary field , operator (biology) , mathematical physics , duality (order theory) , physics , pure mathematics , algebraic number , mathematics , field (mathematics) , theoretical physics , mathematical analysis , geometry , biochemistry , chemistry , repressor , transcription factor , gene

Starting from a chiral conformal Haag-Kastler net on 2 dimensional Minkowski space we construct associated pointlike localized fields. This amounts to a proof of the existence of operator product expansions.We derive the result in two ways. One is based on the geometrical identification of the modular structure, the other depends on a “conformal cluster theorem” of the conformal two-point-functions in algebraic quantum field theory.The existence of the fields then implies important structural properties of the theory, as PCT-invariance, the Bisognano-Wichmann identification of modular operators, Haag duality and additivity

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