Operator Calculus in Quantized Field Theory
Progress of theoretical physics
Following the suggestion of Feynman, we analyze the operators corresponding to the el~tron. 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 dilfusion equation for the Dirac field very simply. The relations to the
... e relations to the Schwinger's new theory of Green function are also discussed. Finally the formula for multiple boson or fermion pair.producrion are presented as illustrations for applications. *) Concerning the principles and techniques of our operator calculus the reader are requested to refer to the Fujiwara's work~l. But we have not gained any new results, since we do not use any new principles and technIques, and it is only a mathematical re·expression of old materials. **) In this paper we use Schwinger's notations9! mainly and take iZ=c=1.