Interaction between two point-like charges in nonlinear electrostatics

We consider two point-like charges in electrostatic interaction between them within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We find the common field of the two charges in a dipole-like approximation, where the separation between them $R$ is much smaller than the observation distance $r:$ with the linear accuracy with respect to the ratio $R/r$, and in the opposite approximation, where $R\gg r,$ up to the the term quadratic in the ratio $r/R$. The consideration fulfilled proposes the law $a+b R^{1/3}$ for the energy, when the charges are close to one another, $R\rightarrow 0$. This leads to the singularity of the force between them to be $R^{-2/3}$, which is weaker than Coulomb law $R^{-2}$.Comment: 20 pages, 1 figur

Collapse of Positronium and Vacuum Instability

A hypercritical value for the magnetic field is determined, which provides the full compensation of the positronium rest mass by the binding energy in the maximum symmetry state and disappearance of the energy gap separating the electron-positron system from the vacuum. The compensation becomes possible owing to the falling to the center phenomenon. The structure of the vacuum is described in terms of strongly localized states of tightly mutually bound (or confined) pairs. Their delocalization for still higher magnetic field, capable of screening its further growth, is discussed.Comment: Talk given at 12th Lomonosov Conference on Elementary Particle Physics, Moscow, August 25-30, 2005 to be published in Proceedings with World Scientific Publishing Co (Singapore). 5 pages. LATEX requires 12 Lomcon.sty and cite.st

Modification of Coulomb law and energy levels of hydrogen atom in superstrong magnetic field

The screening of a Coulomb potential by superstrong magnetic field is studied. Its influence on the spectrum of a hydrogen atom is determined.Comment: Lectures at 39 ITEP Winter School and 11 Baikal Summer School; 12 pages, 5 figure