/ 00 12 02 1 v 2 1 5 Fe b 20 01 Braided Structure in 4 - dimensional conformal Quantum Field Theory

Higher dimensional conformal QFT possesses an interesting braided structure which, different from the d=1+1 models, is restricted to the timelike region and therefore easily escapes euclidean action methods. It lies behind the spectrum of anomalous dimensions which may be viewed as a kind of substitute for a missing particle interpretation in the presence of interactions. 1 Introductory remarks Since the early 60ies the use of conformal field theory in particle physics has been beset by physical doubts concerning incompatibilities with the LSZ framework of interacting (Wigner) particles. Indeed, besides free zero mass particles there are strictly speaking no other conformal situations which are consistent with a particle interpretation [1]. The analytic simplifications of massless limits are (again apart from free situations) in some sense paid for by the conceptual complications within the particle setting; the latter allow at best to extract extremely inclusive scattering data from interacting conformal field theory using a scattering theory which is based on probabilities instead of amplitudes [2] i.e. conformal theory is not directly a theory of particles. Nevertheless, as it is already well known from chiral conformal theories, conformal field theory with its arena of spacetime charge flows and their fusions is presently the most