On the Renormalization in Quantum Electrodynamics

The new renonnalization procedure in quantum electrodynamics is presented in this paper. With this procedure, the finite S-matrix can be automatically obtained by · use of the modified commutation relations and propagation functions and, therefore, without introducing the counter tenns of mass- and charge-types. The various significant features of this new renonnalization procedure are also discussed. § 1. Introductiou and summary As is well known, in the theory of the S-matrix in quantum electrodynamics there appear four infinite constants (ax,~, Z2 and Z:I).1) The contributions of Zl and Z2 ' however, cancel each other in virtue of the Ward's identity ~=Z22), and so the infinities remaining in the final expression of S-matrix are those of ax and Z:l ' which are regarded as the induced mass and charge due to the reaction of the self-field. In the usual renormalization theory these two infinities are removed by means of the counter terms of mass and charge. In the present paper the new renormalization method is presented, in which the introduction of such counter terms is unnecessary. As is well known, the diverging term iJx of the mass type of the electron can be eliminated by means of a canonical transformation, which leads to the result of changin