Heisenberg Equation of Motion Calculation of the Electron Self-Mass in Nonrelativistic Quantum Electrodynamics

Abstract

The calculation of the self-mass of a point electron has been a theoretical problem which many generations of physicists have worked on intensively. Perturbative analyses, carried out either in classical or quantum electrodynamics, nonrelativistically or relativistically, have invariably led to an infinite result. Several years ago, a new approach was given by Moniz and Sharp.⁽¹⁾ Their work was nonperturbative in the sense that the traditional expansion in the fine-structure constant was not utilized, but rather other approximations, which we shall elaborate on later, were used. Their approach was based on the Heisenberg equations of motion. An important conclusion of their studies was that the quantum-mechanical mass shift of the nonrelativistic point electron is zero. The classical mass shift was also shown to vanish.