  Various 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.
