Nonlinear Theory of Fields

Abstract

Suggested modification of the Einstein-Maxwell system, such that Maxwell equations become non-gauge and nonlinear. The theory is based on assumption that observable (i.e., felt by particles) metric is ${\tilde{g}}_{ab}=g_{ab}-l^2{A}_a{A}_b$, where $g_{ab}$ is metric (found from Einstein equations), $A_a$ is electromagnetic potential, and $l$ is fundamental constant of the theory. Specific model of the mass and charge densities of a fundamental particle is considered. As a result, one obtains solutions corresponding to quantized electrical charge with spectrum $q_n=\frac{2n}{3}e$ and $q_n^{\prime }=-\frac{(2n+1)}{3}e$, where $n=0,1,2,...$ Theory predicts Coulomb interaction between electrical charges and masses. Namely, if ($m,e$) and ($m^{\prime },e^{\prime }$) describe masses and electrical charges of two particles respectively, then energy of interaction (in non-relativistic limit) is $V(r)=[e{e}^{\prime }-km{m}^{\prime }-\sqrt{k}(e{m}^{\prime }+e^{\prime }m)]/r$. It follows, then, that the Earth's mass, $M_E$, contributes negative electrical charge, $Q_E=-\sqrt{k}{M}_E$, which explains why primary cosmic rays consist mainly of positively charged particles. One may attribute the fairweather electric field at the Earth's surface to the charge $Q_E$.

withdrawn due to unlikely result