CONFORMAL HAAG-KASTLER NETS, POINT-LIKE LOCALIZED FIELDS AND THE EXISTENCE OF OPERATOR PRODUCT EXPANSIONS

Starting from a chiral conformal Haag-Kastler net on 2 dimensional Min kowski 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 identi fication of the modular structure, the other depends on a ''conformal cluster theorem'' of the conformal two-point-functions in algebraic qu antum held 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 additiv ity.