In order to construct the singularity free classical electrodynamics, Boppll proposed to generalize the field equation and Peier1s·McManus'1l attempted the extension of the interaction; In this' paper, we investigate first the interrelations between these two theories from the quantum-theoretical point of view. Then two special types of the non-local interaction between electromagnetic field and an electron are proposed, with which the problem of the self-charge as well as the electron self-energy can be treated , satisfactorily.
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Shono et al. (1952) studied this question.
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