  In the paper we focus on the study of the functional complexity of the
Lorentz parametrizing functions in connection with the time-reversal
transformations. We argue that the interactions encoded in the corresponding
correlators of non-local quark(-gluon) operators generate additional sources of
functional complexity for the parametrizing functions which are not discussed
in the literature. We also revisit the Lorentz parametrization of different
correlators given by the hadron matrix elements of the non-local operators. The
evidences for the new parametrizing function existence have been presented.
