Conformal Haag-Kastler Nets, Pointlike Localized Fields and the Existence of Operator Product Expansions

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. (orig.)