Related papers: Perturbative series and the 1/N expansion for the …
The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact…
The structure of the QFT expansion is studied in the framework of a new "Invariant analytic" version of the perturbative QCD. Here, an invariant (running) coupling $a(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi$ is transformed into a…
The Gell-Mann -- Low function \beta(g) in QED (g is the fine structure constant) is reconstructed. At large g, it behaves as \beta_\infty g^\alpha with \alpha\approx 1, \beta_\infty\approx 1.
We introduce an extension of a variationally optimized perturbation method, by combining it with renormalization group properties in a straightforward (perturbative) form. This leads to a very transparent and efficient procedure, with a…
An approximation algorithm is proposed to transform truncated QCD (or QED) series for observables. The approximation is a modification of the Baker-Gammel approximants, and is independent of the renormalization scale (RScl) $\mu$ -- the…
Precise extractions of $\alpha_s$ from $\tau\to {\rm (hadrons)}+\nu_\tau$ and from $e^+e^-\to {\rm (hadrons)}$ below the charm threshold rely on finite energy sum rules (FESRs) where the experimental side is given by integrated spectral…
Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a…
It is shown that the commonly accepted relationship between the Landau singularity in the running coupling constant of QED or QCD and the renormalon singularities in the Borel sums of perturbation theory expansions is only a particular…
We present a nonrelativistic one-particle quantum mechanics whose perturbative S-matrix exhibits a renormalon divergence that we explicitely compute. The potential of our model is the sum of the 2d Dirac $\delta$-potential -- known to…
A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We discuss the connection between the…
The large-order behaviour of QCD is dominated by renormalons. On the other hand renormalons do not occur in conformal theories, such as the one describing the infrared fixed-point of QCD at small beta_0 (the Banks--Zaks limit). Since the…
Perturbation series in QCD are generally asymptotic and suffer from so-called infrared renormalon ambiguities. In the context of the standard operator product expansion in MS-bar these ambiguities are compensated by matrix elements of…
The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the…
We elaborate on the relation between perturbative and power-like corrections to short-distance sensitive QCD observables. We confront theoretical expectations with explicit perturbative calculations existing in literature. As is expected,…
To resum large logarithms in multi-scale problems a generalization of $\MS$ is introduced allowing for as many renormalization scales as there are generic scales in the problem. In the new \lq\lq minimal multi-scale subtraction scheme''…
It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties,and contain in particular IR generated ghost poles and cuts. As an outcome the rigorous background perturbation theory is…
We compare the solutions of one-scale Dyson-Schwinger equations in the Minimal subtraction (MS) scheme to the solutions in kinematic (MOM) renormalization schemes. We establish that the MS-solution can be interpreted as a MOM-solution, but…
We present calculations of the leading and O(1/N) terms in a large-N expansion of the \beta-functions for various supersymmetric theories: a Wess-Zumino model, supersymmetric QED and a non-abelian supersymmetric gauge theory. In all cases N…
For $\mathcal{N}=1$ supersymmetric Yang-Mills theory without matter it is demonstrated that there is a class of renormalization schemes, in which the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) formula for the renormalization…
A comprehensive analysis on the photon self-energy, the fermion self-energy, and the fermion vertex function is presented at one loop in the context of quantum electrodynamics (QED) with 1 extra dimension. In 5-dimensional theories,…