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In classical physics, fields move point particles via Newtonian mechanics with Lorentz forces, and particles create fields via Maxwell equations. Both pictures have quite rigorous mathematical theories. However, consistency of united system of these equations had never been proved. In quantum physics QFT seems to cover everything but rigorous QFT does not still exist. Moreover instead, often scattering pictures with virtual particles are used. In this talk classical picture with information transmission (by virtual particle) between two particles will be presented in detail. Unexpectedly, it gives rigorous deduction (without Maxwell equations) of 3-dimensional Coulomb force between two particles in question. Also two rigorous many particle models will be presented: 1. model of electric current, that appears by self-organization in many electron system, interacting via Coulomb force, 2. one-dimensional many particle model of ball lightning