Renormalized field theory from particle theory 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, \[ \mathrm{particle} \Longleftrightarrow \mathrm{particle} , \] was replaced by a new pair of mysteries: how do particles and fields interact without a mediator? \[ \mathrm{particle} \Longleftrightarrow \mathrm{field} \Longleftrightarrow \mathrm{particle} \] But doubling the number of mysteries was not the only problem. Field theory introduced a broad collection of difficulties; divergences and violations