Nobel prize to S. Tomonaga awarded in 1965. Co-winners J. S. Schwinger and R. P. Feynman "for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles''
Tati, T.; Tomonaga, S.; A Self-Consistent Subtraction Method in the Quantum Field Theory. I.
Progr. of Theor. Phys. 3 (1948) 391;
As is well known the present formalism of the quantum field theory contains a fundamental defect which reveals itself most directly in the infinite self-energy of elementary particles. The infinities of the same nature appear also when one deals with collision problems involving field reactions, e.g. radiative correction to the cross section for the elastic scattering of an electron in an external field of force. As was discussed by Pauli and Fierz in the nonrelativistic case and by Dancoff in the
relativistic, the correction due to the radiation reaction in the latter problem turned out infinite. Such a circumstance implies that the satisfactory solution of this problem would be only reached when the fundamental difficulty of the current quantum field theory has found its ultimate solution. In such a situation, one used to resort to some procedure to get rid of the difficulty, such as cutting off of high frequency effects or subtracting infinite terms by a suitable prescription.
But it goes without saying that such procedures are only makeshifts far from true solution having neither theoretical basis nor any connection with experimental facts. A remarkable progress was brought about; however, when Lamb and Retherford confirmed the level-shift of the hydrogen atom by their ingenious experiment and Schwinger, Weisskopf, Oppenheimer and Bethe gave its theoretical interpretation in terms of the radiative reaction. Especially Bethe proposed a method how to manage the infinity
in this problem and enabled us to treat the field-reaction problem for the first time in close connection with reliable experimental data ... It becomes thus desirable to obtain a relativistic generalization of the canonical transformation of Pauli and Fierz and find a general prescription to separate the infinite terms which can be amalgamated into the mass of the electron. In this and the following papers it will be shown that such a generalization is in fact possible, and the field reaction
problems can be treated in a consistent way without touching the inherent infinities of the current quantum field theory.
Related references More (earlier) information appears in S. Tomonaga, Progr. of Theor. Phys. 1 (1946) 27;
Z. Koba, T. Tati, and S. Tomonaga, Progr. of Theor. Phys. 2 (1947) 198;
Z. Koba, T. Tati, and S. Tomonaga, Progr. of Theor. Phys. 2 (1947) 101;
See also H. A. Bethe, Phys. Rev. 72 (1947) 339;
F. Bloch and A. Nordsieck, Phys. Rev. 52 (1937) 54;
V. F. Weisskopf, Phys. Rev. 56 (1939) 72;
Z. Koba and S. Tomonaga, Progr. of Theor. Phys. 3 (1948) 208;
Z. Koba and G. Takeda, Progr. of Theor. Phys. 3 (1948) 98;
Z. Koba and G. Takeda, Progr. of Theor. Phys. 3 (1948) 203;
Z. Koba and G. Takeda, Progr. of Theor. Phys. 3 (1948) 387;
H. W. Lewis, Phys. Rev. 73 (1948) 173;
S. T. Epstein, Phys. Rev. 75 (1949) 177;
J. Schwinger, Phys. Rev. 73 (1948) 416;
W. E. Lamb and R. C. Retherford, Phys. Rev. 72 (1947) 241;
S. M. Dancoff, Phys. Rev. 55 (1939) 959;
W. Pauli and M. Fierz, Nuovo Cim. 15 (1938) 167;
Z. Koba and S. Tomonaga, Progr. of Theor. Phys. 2 (1947) 218;
Creation of the covariant quantum electrodynamic theory. Tomonaga method.