Problem definition

The self-energy of the electron is the energy of the electromagnetic field which is generated by the electron in addition to the energy of the interaction of the electron with this field. Waller, Oppenheimer, and Rosenfeld calculated the self-energy of the free electron by means of the Dirac relativistic wave equation of the electron and the Dirac theory of the interaction between matter and light. They here used an approximation method which represents the self-energy in powers of the charge e. They found that the first term, which is proportional to e2, already becomes infinitely large. The essential reason for this is that the theory of the interaction of the electron with the electromagnetic field is built on the classical equations of motion of a point shaped electron whose self-energy, as is well known, also becomes infinite in classical theory.

In the present note, the expressions for the self-energy shall be derived without direct application of quantum electrodynamics, but by means of the Heisenberg radiation theory, which is linked much more closely to classical electrodynamics.