Absence of runaways and divergent self-mass in nonrelativistic quantum electrodynamics

Abstract

We derive the quantum-mechanical operator equation of motion for a point electron and show that (i) the electrostatic self-mass of a point electron is zero in quantum mechanics; (ii) the equation of motion does not admit runaway solutions; (iii) the correspondence limit of the solutions of the quantum-mechanical equation likewise does not display runaways; and (iv) the solutions do not violate the principle of causality in quantum mechanics.