相关论文: Borel summation and momentum-plane analyticity in …
We investigate the analytic structure of the Borel-summed perturbative QCD amplitudes in the complex plane of the coupling constant. Using the method of inverse Mellin transform, we show that the prescription dependent Borel-Laplace…
After reviewing basic facts about large-order behaviour of perturbation expansions in various fields of physics, I consider several alternatives to the Borel summation method and discuss their relevance to different physical situations.…
We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from…
Relation between the infrared renormalons, the Borel resummation prescriptions, and the analyticity structure of Green functions in perturbative QCD (pQCD) is investigated. A specific recently suggested Borel resummation prescription…
Using a full resummation of the Adler function in the large-$\beta_0$ approximation of QCD and a mathematical framework of resurgence suitable for the specific properties of the Borel transform in this particular case, we derive a compact…
Methods of summation of power series relevant to applications in quantum theory are reviewed, with particular attention to expansions in powers of the coupling constant and in inverse powers of an energy variable. Alternatives to the Borel…
The technique of conformal mappings is applied to enlarge the convergence of the Borel series and to accelerate the convergence of Borel-summed Green functions in perturbative QCD. We use the optimal mapping, which takes into account the…
We give an explicit demonstration that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B\to iE…
Exact large-$N_{f}$ results for the QCD Adler $D$-function and Deep Inelastic Scattering sum rules are used to resum to all orders the portion of QCD perturbative coefficients containing the highest power of…
Thesis includes review on the large order behaviour of perturbation theory in quantum mechanical and field theory models; generalization of the Borel summability and strong asymptotic conditions to various (including horn-shaped) regions;…
The quark form factor is known to exponentiate within the framework of dimensionally regularized perturbative QCD. The logarithm of the form factor is expressed in terms of integrals over the scale of the running coupling. I show that these…
The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a…
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…
A new method of estimating higher order perturbative coefficients is discussed. It exploits the rapid, asymptotic growth of perturbative coefficients and the information on the singularities in the complex Borel plane. A comparison with…
We discuss the method of conformal mappings applied to perturbative QCD. The approach is based on the Borel-Laplace integral regulated with the principal value prescription and the expansion of the Borel transform in powers of the variable…
The bilocal expansion of Borel transform provides an efficient way of Borel resummation with low order perturbations in QCD. Its applications to the heavy quark pole mass, static potential, and lattice calculation are reviewed.
In this paper, we consider the resummation of the divergent Rayleigh-Shrodinger perturbation expansion for the ground state energy of the quartic anharmonic oscillator in one dimension. We apply the Borel-Pade resummation method combined…
Starting from the divergence pattern of perturbative quantum chromodynamics, we propose a novel, non-power series replacing the standard expansion in powers of the renormalized coupling constant $a$. The coefficients of the new expansion…
Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…
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…