相关论文: Resummation of not summable series

We generalize the notion of an asymptotic weak coupling expansion about an exactly solvable model in quantum mechanics and quantum field theory to an all positive value coupling convergent expansion. This is done by rescaling the variables…

We demonstrate that certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem and using principles of quantum mechanics. For simplicity we illustrate the method by exploring the…

An alternative multipole expansion of the correlation term is derived. Modified spherical Bessel type functions which simplify as a summation of multiple orders of basic trigonometric functions are generated from this new method. We use…

We present new results on the summation of nonpower-series expansions in QCD Analytic Perturbation Theory (APT) in the one-loop approximation. We show how to generalize the approach suggested by one of us earlier to the cases of APT and…

Motivated by recent efforts to bridge between weak-field and strong-field descriptions of black-hole binary dynamics, we develop a resummation scheme for post-Minkowskian radiative observables in extreme-mass-ratio scattering, augmented…

A method for renormalization of the Casimir energy of confined fermion fields in (1+1)D is proposed. It is based on the extraction of singularities which appear as poles at the point of physical value of the regularization parameter, and…

Methods of Borel integration to calculate the binding ground energies and mass of b-barb quarkonia are presented. The methods take into account the leading infrared renormalon structure of the "soft" binding energy E(s) and of the quark…

We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the…

With a parametric form of the equation of state parameter of dark energy, a quintessence potential has been reconstructed. The potential is found to be a generalization of a double exponential potential. The constraints on the parameters…

We develop a series of resonant short-range two-boson potentials reproducing the same two-body low-energy observables and apply them in three- and four-body calculations. We demonstrate that the universal behavior predicted by effective…

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.…

Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…

We extend the analysis of the Bogoliubov free energy functional to two dimensions at very low temperatures. For sufficiently weak interactions, we prove two term asymptotics for the ground state energy.

It had been known that the Borel transforms of the twice quark pole mass 2*mq and of the QCD q-barq static potential V(r) have leading infrared renormalons at b=1/2 such that they cancel in the sum. The renormalon residue of 2*mq had been…

A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…

We compare and contrast three different perturbative expansions for the quartic anharmonic oscillator wavefunction and apply a modified Borel summation technique to determine the energy eigenvalues. In the first two expansions this provides…

Monopole bubbling effect is screening of magnetic charges of singular Dirac monopoles by regular 't Hooft-Polyakov monopoles. We study properties of weak coupling perturbative series in the presence of monopole bubbling effects as well as…

The improvement of resummation algorithms for divergent perturbative expansions in quantum field theory by asymptotic information about perturbative coefficients is investigated. Various asymptotically optimized resummation prescriptions…

The divergent perturbative expansion of the free-energy density of thermal SU(3) gauge theory is resummed into a rapidly convergent series using a novel, variational, implementation of the method of conformal mapping of the corresponding…

We calculate the multi-instanton corrections to the ground state energy in large $N$ Matrix Quantum Mechanics. We find that they can be obtained, through a non-perturbative difference equation, from the multi-instanton series in…