Renormalization group, causality, and nonpower perturbation expansion in QFT

The structure of the QFT expansion is studied in the framework of a new "in variant analytic" version of the perturbative QCD. Here, an invariant coupl ing 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), whi ch, by construction. is free of ghost singularities because it incorporates some nonperturbative structures. In the framework of the "analyticized" pe rturbation theory, an expansion fbr an observable F, instead of powers of t he 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 res ults in weak loop and scheme dependences. Because of the analyticity requir ement, the perturbation series for F(x) becomes an asymptotic expansion a l a 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 .