Abstract
Following the suggestion of Feynman, we analyze the operators corresponding to the electron-positron field by means of the operator calculus. Thus we can deduce operationally Feynman's theory from the second quantized theory. With the aid of the external spinors, which are considered as the analogues of the Schwinger's prescribed source, we obtain formally a closed form of the S-matrix. Using this result we can derive the diffusion equation for the Dirac field very simply. The relations to the Schwinger's new theory of Green function are also discussed. Finally the formula for multiple boson or fermion pair-production are presented as illustrations for applications.
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