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A. I. Breev

Publications and source records attributed to A. I. Breev.

23 records · Page 2Linked to original sources
arXiv2017

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 $R^{-2}$.

physics.class-ph↗
arXiv2016

Discreteness of Point Charge in Nonlinear Electrodynamics

We consider two point charges in electrostatic interaction between them within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We argue that if the two charges are equal to each other the repulsion force between them disappears when they are infinitely close to each other, but remains as usual infinite if their values are different. This implies that within any system to which such a model may be applicable the point charge is fractional, it may only be $2^n$-fold of a certain fundamental charge, n=0,1,2... We find the common field of the two charges in a dipole approximation, where the separation between them is much smaller than the observation distance.

hep-th↗
arXiv2015

The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration

Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operator

math-ph↗
arXiv2014

Yang-Mills gauge fields conserving the symmetry algebra of the Dirac equation in a homogeneous space

We consider the Dirac equation with an external Yang-Mills gauge field in a homogeneous space with an invariant metric. The Yang-Mills fields for which the motion group of the space serves as the symmetry group for the Dirac equation are found by comparison of the Dirac equation with an invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The eigenfunctions and the corresponding eigenvalues for the Dirac equation are obtained in the space $\mathbb{R}^2\times \mathbb{S}^2$ by a noncommutative integration method.

gr-qc↗