The Theory of Anomalous Scale Dimensions

Using the 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 which necessarily have an anomalous contribution in addition to their canonical scale-dimensions, we set out to construct a classification theory for the spectra of anomalous dimensions. We find that they are resulting from a braid group structure. The latter is however not related to statistics (spacelike interchange) but rather draws its raison d’etre from the timelike Huygens principle (timelike commutativity), a characteristic property of conformal observables, as well as from the existence of a timelike ordering. The global aspects of this Huygens structure also leads to a timelike global charge transport around the Dirac-Weyl compactified Minkowski world M̄ which in turn is inexorably related with an S-T modular SL(2,Z) group structure. 1 Background and preview of new results It had been known for a long time that conformal quantum field theory exhibits in addition to the general spin-statistics theorem another more characteristic structural property which we will refer to as the “anomalous dimension-central phase” connection. It relates the anomalous scale dimension of fields modulo integers (semi-integers in the case of Fermion fields) to the phase obtained by performing one complete timelike sweep around the compactified Minkowski world [1] and hence is analogous to the relation of the spin value related to a spatial rotation sweep to the statistics phase [2] of the spin-statistics connection including chiral conformal field theory where the rotation around S is lightlike. The word “central” here refers to the center Z( ̃ SO(d, 2)) of the infinite sheeted covering group ̃ SO(d, 2) which has one abelian generator for