© 2015 Physics Essays Publication. A special relativity action for a system of point charged particles is proposed with the particularity of being complete, covariant, and nonstandard; that is, by considering that the action is stationary with respect to small variations of the trajectories of the charges zl i and the electromagnetic potential Aa ?xb ?, the equations of motions for each particle including the selfforces and the Maxwell equations are deduced. Without using any constraint, a Hamiltonian density is obtained whose corresponding Hamilton equations describe the equations of motion including the self-forces and the Maxwell equations too.
De Parga, G. A., Domínguez-Hernández, S., & Salinas-Hernández, E. (2015). Hamiltonian density for a point charged particles system in special relativity. Physics Essays, 550-560. https://doi.org/10.4006/0836-1398-28.4.550