We discuss the new model expressionᾱ an (Q 2 ) recently obtained for the QCD running coupling with a regular ghost-free behavior in the "low Q 2 " region. Being deduced from the standard "asymptotic-freedom" expression by imposing the Q 2 -analyticity -without any adjustable parameters -it obeys nice features: (i) The universal limiting valueᾱ an (0) = 4π/β 0 ≃ 1.4 expressed only via group symmetry factors and independent of experimental estimates on the running couplingᾱ s (Q 2 ) (of QCD scale parameter Λ). This value turns out to be stable with respect to higher order corrections; (ii) Stability of IR behavior with respect to higher-loop effects; (iii) Coherence between the experimentalᾱ an (M 2 τ ) value and integral information on IRᾱ s (Q 2 ) behavior as extracted from jet physics data.

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We argue that a technique called analytic perturbation theory leads to a well-defined method for analytically continuing the running coupling constant from the spacelike to the timelike region, which allows us to give a selfconsistent definition of the running coupling constant for timelike momentum.The corresponding β-function is proportional to the spectral density, which confirms a hypothesis due to Schwinger.

We investigate a new "renormalization invariant analytic formulation" of calculations in quantum chromodynamics, where the renormalization group summation is correlated with the analyticity with respect to the square of the transferred momentum Q 2 . The expressions for the invariant charge and matrix elements are then modified such that the unphysical singularities of the ghost pole type do not appear at all, being by construction compensated by additional nonperturbative contributions. Using the new scheme, we show that the results of calculations for a number of physical processes are stable with respect to higher-loop effects and the choice of the renormalization prescription.Having in mind applications of the new formulation to inelastic lepton-nucleon scattering processes, we analyze the corresponding structure functions starting from the general principles of the theory expressed by the Jost-Lehmann-Dyson integral representation. We use a nonstandard scaling variable that leads to modified moments of the structure functions possessing Källén-Lehmann analytic properties with respect to Q 2 . We find the relation between these "modified analytic moments" and the operator product expansion.Take care of the Principles, and the Principles shall take care of you.Scientific achievements of Nikolai Nikolaevich Bogoliubov are characterized by a unique combination of determination in solving concrete scientific problems and a high level of mathematical culture. He could find the shortest path to a physical result using most general principles of the theory.The renormalization-invariant analytic approach to quantum chromodynamics exposed here and its most recent applications are based on the works [1,2,3,4] by Bogoliubov with his closest collaborators. A characteristic feature of these investigations is their strong relation with the fundamental quantum physics principles.