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''
Koba, Z.; Tati, T.; Tomonaga, S.; On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields. II. Case of Interacting Electromagnetic and Electron Fields
Progr. of Theor. Phys. 2 (1947) 101;
The aim of the present paper is to apply our method of formulation to the quantum electrodynamics which deals with the electromagnetic field interacting with the electron field. Although we have in the case of quantum electrodynamics a perfectly relativistic formalism, that is Dirac's many-time theory, (P. A. M. Dirac, V. Fock and B. Podolsky, Physik Zeits. Sow. 2 (1932) 468) it will be nevertheless of some importance to formulate the theory also in our formalism, since the former,
in which the states of electrons are described in the configuration space, applies only to the case where the number of the electrons does not change, and is thus incapable of dealing with such phenomena as the emission of -rays or the decay of mesons emitting electrons, without introducing a rather unfavourable complication into the theory at the sacrifice of its beautifulness. It is, therefore, desirable to treat the electrons as a quantized field and not
as particles, since the former treatment fits the cases better in which the number of the electrons really changes. It is already nearly known in I how to apply our formalism to the quantum electrodynamics except the well-known complication due to the existence of the so-called auxiliary condition. One of the main tasks in the present paper is thus to find the auxiliary condition in our formalism and to eliminate it in a relativistically invariant way on the lines which has been reported by
Hayakawa, Miyamoto and one of the authors in another place.
Related references More (earlier) information appears in S. Tomonaga, Riken Iho 22 (1943) 525;
S. Tomonaga, Progr. of Theor. Phys. 1 (1946) 27;
See also P. A. M. Dirac, V. A. Fock, and B. Podolsky, Physik Zeits. Sow. 2 (1932) 468;
Creation of the covariant quantum electrodynamic theory. Tomonaga method.