2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58376Various models of charged particles interacting with a quantized, ultraviolet cutoff radiation field (but not with each other) are investigated. Upper and lower bounds are found for the self- or ground state-energies without mass renormalization. For $N$ fermions the bounds are proportional to $N$, but for bosons they are sublinear, which implies `binding', and hence that `free' bosons are never free. Both `relativistic' and non-relativistic kinematics are considered. Our bounds are non-perturbative and differ significantly from the predictions of perturbation theory.16 pages, Latex, Replaces the version of August 20, 1999. A clarifying paragraph about perturbation theory was added after equation 1.6Mathematical PhysicsHigh Energy Physics - Theory81V10, 81V70 (Primary); 81V45, 81T08, 81T16 (Secondary)text