Classical Lorentz-invariant theory of systems with self-action: Lagrangian formulation

A Lorentz-invariant theory of singular Lagrangian particle systems with selfaction, treated as a dependence of the Lagrangian upon acceleration, is developed. The Lagrangian equations and their exact special solutions are found. The first integrals of 4-momentum and angular momentum are calculated. Particles possessing weak self-action are treated as classical analogs of particles with half-integral spin.