Renorm-group, Causality and Non-power Perturbation Expansion in QFT

Abstract The structure of the QFT expansion is studied in the framework of a new “Causal analytic version” of the perturbation theory. Here, the leading idea is to combine the renormalization group (RG) invariance with a general property of causality expressed in the form of the Q2–analyticity. This combining is performed by a special procedure, “analytization”. The procedure, first proposed in the 50-ies, matches the Q2–analyticity with the RG invariance by incorporating some nonperturbative structures. We consider the case of quantum chromodynamics (QCD). Here, the central object, an invariant coupling a(Q2/Λ2) = β1αs(Q 2)/4π , is transformed into a “Q2–analytized” invariant (running) coupling aan(Q 2/Λ2) ≡ A(x) , which, by constuction, is free of ghost singularities. It correlates experimental data. Meanwhile, the “analytized” perturbation expansion for an observable F , in contrast with the usual case, may contain specific functions An(x) = [a(x)]an , the “n-th power of a(x) analytized as a whole”, instead of (A(x)) n . In other words, the pertubation series for F (x), due to causality imperative, may change its form turning into an asymptotic expansion over a nonpower set {An(x)} . We analyse sets of functions {An(x)} and discuss properties of non-power expansion arising with their relations to feeble loop and scheme dependence of observables. The issue of ambiguity of the Causal analytization procedure and of possible inconsistency of some of its versions with the RG structure is also discussed.