Related papers: Distributional Borel Summability for Vacuum Polari…
It is proved that the divergent Rayleigh-Schrodinger perturbation expansions for the eigenvalues of any odd anharmonic oscillator are Borel summable in the distributional sense to the resonances naturally associated with the system.
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…
The Borel summability in the distributional sense is established of the divergent perturbation theory for the ground state resonance of the quantum H\'enon-Heiles model.
We present a method for extracting tunnelling amplitudes from perturbation expansions which are always divergent and not Borel-summable. We show that they can be evaluated by an analytic continuation of variational perturbation theory. The…
We present a method for evaluating divergent non-Borel-summable series by an analytic continuation of variational perturbation theory. We demonstrate the power of the method by an application to the exactly known partition function of the…
We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasi-periodic analytic forcing term and in the presence of damping. As a physical application one can think of a…
The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for…
The exact solutions of the wave equation for arbitrary spin particles with electric dipole and magnetic moments in the constant and uniform electromagnetic field were found. The differential probability of pair production of particles by an…
We consider a class of $n^{\text{th}}$-order linear ordinary differential equations with a large parameter $u$. Analytic solutions of these equations can be described by (divergent) formal series in descending powers of $u$. We demonstrate…
The electric and magnetic fields are investigated on the basis of quantum vacuum. The analysis of the electromagnetic energy and force indicates that an electric field is a polarized distribution of the vacuum virtual dipoles, and that a…
The string-inspired technique is used for a first calculation of the one-loop axialvector vacuum polarisation in a general constant electromagnetic field. A compact result is reached for the difference between this tensor and the…
Simple sufficient conditions are given that ensure the uniform continuity in distribution for Borel transformations of random fields.
It is common practice to take for granted the equality (up to the constant $\varepsilon_0$) of the electric displacement ($\bf{D}$) and electric ($\bf{E}$) field vectors in vacuum. The same happens with the magnetic field ($\bf{H}$) and the…
The theory for large amplitude circularly polarized waves propagating along an external magnetic field is extended in order to include also vacuum polarization effects. A general dispersion relation, which unites previous results, is…
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
The effects of electric field polarizations on pair production from a vacuum are investigated numerically by employing the real-time Dirac-Heisenberg-Wigner formalism. For few-cycle fields, it is found that the interference pattern in…
A weighted sums of squares decomposition of positive Borel measurable functions on a bounded Borel subset of the Euclidean space is obtained via duality from the spectral theorem for tuples of commuting self-adjoint operators. The analogous…
We consider a quartic O(N)-vector model. Using the Loop Vertex Expansion, we prove the Borel summability in 1/N along the real axis of the partition function and of the connected correlations of the model. The Borel summability holds…
A modification of perturbation theory, known as delta-expansion (variationally improved perturbation), gave rigorously convergent series in some D=1 models (oscillator energy levels) with factorially divergent ordinary perturbative…
A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is…