2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144413The momentum of a free massive particle, invariant under translation, thereby realizes a trivial representation of the translation group. By allowing nontrivial reps of translations, momentum changes with translation, a recipe for force. Here the procedure is applied to the conventional construction of a free quantum field using spacetime symmetries, yielding a more general field with the free field as a special case. It is shown that a particle described by the quantum field follows the classical trajectories of a massive charged particle in electromagnetic and gravitational fields.19 pages, no figures, 5 problems. Minor editing. Wording changes: `interval' replaced by `coordinate difference' where appropriate. A relic phrase from earlier versions dropped. Results, equations are unchangedHigh Energy Physics - Theorytext