Anomalous scale dimensions from time-like braiding

Using previously gained insight about the particle/field relation in conformal quantum field theories, which required interactions to be related to the existence of particle-like states associated with fields of anomalous scaling dimensions, we set out to construct a classification theory for the spectra of anomalous dimensions. Starting from the old observations on conformal superselection sectors related to the anomalous dimensions via the phases which appear in the spectral decomposition of the centre of the conformal covering group Z(SO(d, 2))-tilde, we explore the possibility of a time-like braiding structure consistent with the time-like ordering which refines and explains the central decomposition. We regard this as a preparatory step in a new construction attempt of interacting conformal quantum field theories in d=4 spacetime dimensions. Other ideas of constructions based on the AdS5-CQFT4 or the perturbative SYM approach in their relation to the present idea are briefly mentioned. (author)