Contrary to conventional wisdom that pretends that particle theory has been disproved and replaced by field theory, we demonstrate that the Hamiltonian particle theory gives an improved version of the usual field-theoretic Hamiltonian, without the difficulties associated to divergences. Moreover, the particle theory is formulated in base to physical charges and masses of particles, whereas field theory only can use unphysical bare quantities. Newton introduced a model of instantaneous direct interactions among massive particles. This model was latter replicated by Coulomb for charged particles and became known as action-at-a-distance; an unfortunate name has generated unending polemics among physicists and philosophers. A better name is direct-particle-interaction . Physicists, dissatisfied with the action-at-distance model of interactions, introduced a contact-action model based in fields. The mystery on how one particle interacts with other particle without a mediator, \[ \mathrm{