Forcing Free Fields

Quantum fields with arbitrary spin for massive particles are derived using spacetime symmetry. We note that assigning equivalent eigenstates at separate events in spacetime determines a representation of translation. For the most general translation representations, translation changes momentum. Force is implicit when momentum differs for equivalent eigenstates at separate events. Next, since intervals are invariant under translation through any displacement, any displacement can be associated with the translation of quantum states when a translation along a given displacement is applied to spacetime. Gravity can be included because the displacement applied to quantum states can have an arbitrary linear dependence on the displacement applied to spacetime. Lastly, classical trajectories are paths of extreme phase. It is shown that a particle described by the quantum field follows the classical trajectories of massive charged particles in background electromagnetic and gravitational fields. PACS: 11.30.Cp Lorentz and Poincare invariance; 03.70.+k Theory of quantized fields 04.60.-m Quantum gravity; ∗affiliation and mailing address: Department of Applied Mathematics and Sciences, Wentworth Institute of Technology, 550 Huntington Avenue, Boston, MA, USA, ZIP 02115, telephone number: (617) 989-4338, e-mail address: [email protected]