Communications in Mathematical Physics

, Volume 176, Issue 3, pp 541–554 | Cite as

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

  • Klaus Fredenhagen
  • Martin Jörß


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.


Neural Network Statistical Physic Field Theory Complex System Quantum Field Theory 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Klaus Fredenhagen
    • 1
  • Martin Jörß
    • 1
  1. 1.II. Institut für Theoretische Physik der Universität HamburgHamburgGermany

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