Conformal covariance of massless free nets

In the present paper we review in a fibre bundle context the covariant and massless canonical representations of the Poincaré group as well as certain unitary representations of the conformal group (in 4 dimensions). We give a simplified proof of the well–known fact that massless canonical representations with discrete helicity extend to unitary and irreducible representations of the conformal group mentioned before. Further we give a simple new proof that massless free nets for any helicity value are covariant under the conformal group. Free nets are the result of a direct (i.e. independent of any explicit use of quantum fields) and natural way of constructing nets of abstract C*–algebras indexed by open and bounded regions in Minkowski space that satisfy standard axioms of local quantum physics. We also give a group theoretical interpretation of the embedding I that completely characterizes the free net: it reduces the (algebraically) reducible covariant representation in terms of the unitary canonical ones. Finally, as a consequence of the conformal covariance we also mention for these models some of the expected algebraic properties that are a direct consequence of the conformal covariance (essential duality, PCT–symmetry etc.). On leave from Mathematical Institute, University of Potsdam, Am Neuen Palais 10, Postfach 601 553, D–14415 Potsdam, Germany.