$p^{2}=m^{2}$ whose generating local fields have an anomalous non-integer (non-semi-integer in the case of Fermion fields) contribution to their long distance behavior. In a CQFT long and short distance behavior coalesce and the accumulation of spectral weight at $p^{2}=0\,$ which becomes related to the anomalous dimension of operators is the vestige of the particle interaction in the massive parent theory from which the CQFT arose by taking the scale-invariant limit. This structure is the collective effect of a total collapse of all multiparticle thresholds on top of each other. The standard LSZ large time scattering limit does not commute with this scaling limit, in fact the LSZ limit of such fields vanishes. It is believed that in order to re-extract from such a situation anything which resembles particle physics one has to apply a more general form of scattering theory [@Bu] which is based on expectation values and probabilities for inclusive cross sections (where outcoming “stuff” below a prescribed energy-momentum resolution is not registered) rather than on amplitudes. But it is presently not clear how one can achieve this. In the case of infraparticles (the electron in QED which is inexorably linked to its photon-cloud) where one also meete a situation of coalescing thresholds, this generalized scattering theory is known to be very useful [@Bu].

Recently there has been a quite different and conceptually[^1] less ambitious but formally quite attractive idea which promises to strengthen the utility of CQFT for particle physics and which is presented in the third section. It basically consists in finding a theory which radically reprocesses the spacetime interpretation and degrees of freedom of CQFT in such a way that now the “energy momentum vector” $R_{\mu }$ of the Dirac-Weyl compactified world $\bar{M}$ becomes the bona fide energy momentum instead of $P_{\mu }$ which in standard canonical or functional terminology means that $R_{\mu }$ is the one related to an action and not $P_{\mu }$. If one