Proofs have been given that the underlying background of the scale-breaking contributions of the Pauli-Jordan functions and of the Feynman propagators is the existence of an energy dependent dispersion of the canonical scale dimension, respectively. The energy dependence of these dispersions can be established by taking into account the existence of the time dispersion, too. For the interacting fields the above functions are subject to the scale invariance restoration around the underlying proper-time dispersions, in so far as the short space-like (...) space-time region is considered. (shrink)