Quantum Theory of the Point Electron. I

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Abstract
A new treatment of the quantum theory of the electromagnetic field is discussed. The interactions between the particles and their interactions with the radiation field are treated according to the ideas of the author's classical theory. The radiation field is taken as a difference of two fields analogous to the field of the Heisenberg-Pauli electrodynamics. The commutation rules for the radiation field differ essentially from those of the Heisenberg-Pauli electrodynamics. In our formalism it is possible to avoid all the divergences by a suitable choice of the wave function of the system particles plus field. The physically relevant wave functions satisfy wave equations similar to those of systems with finite numbers of degrees of freedom, although they are also exact solutions of the Schrödinger equation of the system particles plus field which has an infinite number of degrees of freedom. There is also the possibility of getting finite non-vanishing self-energies.

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