Abstract

The Purpose of this paper is to extend the quantum electrodynamics of the New Field theory to include the dynamics of charged particles. The work of Born and Infeld (Born 1934; Born and Infeld 1934 a , b , 1935) in which the theory has been developed, and of weiss (1936), has dealt with the quantum theory of the electromagnetic field alone, without allowing for the occurrence of point charges; this is inherent in their equation div D = 0. In a Previous paper (1936 a ), the present author has given a classical (i. e. non-quantum) treatment of the dynamics of point charges in the frame of the New Field theory. The analytical methods of that paper were chosen in such a way that they could be used in the generalization to a quantum-mechanical theory, and we shall here use them as the scaffolding for the present work. We shall therefore use the same notation as before. The more important symbols have the following meanings:

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