Relativistic Dynamics of a Charged Particle in an Electroscalar Field

This article devoted to relativistic dynamics of a charged massive particle in an electroscalar field. It represents a continuation of paper [1] where the authors constructed a non-relativistic theory which describes transverse electromagnetic waves along with longitudinal electroscalar ones, responsible for the wave transport of the Coulomb field. A new type of relativistic force exerted by electroscalar field on an electrically charged particle and the relativistic law of superposition of electromagnetic transverse and electroscalar longitudinal fields are established. Also, a relativistically invariant form of a Lagrangian describing the interaction between an electroscalar field and massive electrically charged particle is defined.