Nonlinear Theory of Fields

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. The idea, that mass and charge densities of elementary particles could be functions of electromagnetic potential and background metric only is accepted, and specific model of the densities is considered. As a result, one obtains solutions corresponding to quantized electrical charge with spectrum $q_{n} = {{2n}\over3}e$ and $q'_{n} = -{(2n+1)\over3}e$, where $n = 0, 1, 2, >...$ Theory predicts Coulomb interaction between electrical charges and masses. Namely, if ($m, e$) and ($m',e'$) describe masses and electrical charges of two particles respectively, then energy of interaction (in non-relativistic limit) is $V(r) = [ee' - kmm' - \kappa(em' + e'm)]/r$. It follows, then, that the Earth's mass, $M_E$, contributes negative electrical charge, $Q_E = - \kappa M_E$, which explains why primary cosmic rays consist mainly of positively charged particles. Attributing the fairweather electric field at the Earth's surface to the charge $Q_E$, one obtains an estimat