Self-energy of electrons in non-perturbative QED, Differential equations and mathematical physics

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.