An Approach to the Formulation of Quantum Electrodynamics without Use of Indefinite Metric

概要

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The aim of this paper is to present a new approach to the formulation of the quantum electrodynamics without using indefinite metric, and the program is examined to the third order in the perturbation expansion. As the wave function of free photons, we adopt the representation in which only the transverse components take part, and the second quantization is performed by Fock-Cook-Friedrichs' method. The first order interaction Hamiltonian is so determined as to correspond to that of the transverse photon in the conventional field theory. The Coulomb interaction is introduced as a second order additional term which is necessitated by the covariance requirement of the theory. As for the second order divergences which correspond to the self-energy of the photon and to the renormalization of the electron wave function in the conventional theory, it is shown that the counter terms are necessarily introduced from the requirement of covariance only. The divergence corresponding to the renormalization of the photon wave function does not appear. To treat the divergence of the self-energy of the electron, an additional counter term must be added as it is done in the usual theory. As regards the third order vertex part, it is shown that the correct value of the anomalous magnetic moment is obtained, though some new feature appears in the divergent part.
理論物理学刊行会の論文
1964-02-25