Renormalization group, causality, and nonpower perturbation expansion in QFT

The structure of the QFT expansion is studied in the framework of a new "invariant analytic" version of the perturbative QCD. Here, an invariant coupling constant a(Q(2)/Lambda(2)) = beta(1)alpha(s)(Q(2))/(4 pi) becomes a Q(2)-analytic invariant function a(an)(Q(2)/Lambda(2)) equivalent to A(x), which, by construction. is free of ghost singularities because it incorporates some nonperturbative structures. In the framework of the "analyticized" perturbation theory, an expansion fbr an observable F, instead of powers of the analytic invariant charge A(x), may contain specifier functions An(x) = [a(n)(x)](an) the "nth power of a(x) analyticized as a whole." Functions A(n>2)(x) for small Q(2) less than or equal to Lambda(2) oscillate, which results in weak loop and scheme dependences. Because of the analyticity requirement, the perturbation series for F(x) becomes an asymptotic expansion a la Erdelyi using a. nonpower set (A(n)(x)). The probable ambiguities of the invariant analyticization procedure and the possible inconsistency of some of its versions with the renormalization group structure are also discussed.