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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'' |  |
TOMONAGA 1943
Tomonaga, S.;
On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields
RI 22, 525 (1943);
Progr. of Theor. Phys. 1 (1946) 27;
Reprinted in
(translation into English) Prog. Theor. Phys. 1 (1946) 27.
Selected Papers on Quantum Electrodynamics, editor J. Schwinger, Dover Publications, Inc., New York (1958) 156.
Summary
We have thus shown that the quantum theory of wave fields can be really brought into a form which reveals directly the invariance of the theory against Lorentz transformations. The reason why the ordinary formalism of the quantum field-theory is so unsatisfactory lies in the fact that one has built up this theory in the way which is too much analogous to the ordinary nonrelativistic mechanics. In this ordinary formalism of the quantum theory of fields the theory is divided into two distinct sections:
the section giving the kinematical relations between various quantities at the same instant of time, and the section determining the causal relations between quantities at different instants of time. Thus the commutation relations (1) belong to the first section and the Schrödinger equation (2) to the second.
As stated before, this way of separating the theory into two sections is very unrelativistic, since here the concept "same instant of time'' plays a distinct role.
Also in
our formalism the theory is divided into two sections. But now the separation is introduced in another place: In our formalism the theory consists of two sections, one of which gives the laws of behavior of the fields when they are left alone, and the other of which gives the laws determining the deviation from this behavior due to interactions. This way of separating the theory can be carried out relativistically.
Although in this way the theory can be brought into more satisfactory form,
no new contents are added thereby. So, the well known divergence difficulties of the theory are inherited also by our theory. (Extracted from the introductory part of the paper.).
Related references
See also
H. Yukawa, Kagaku 12 (1924) 251, 282, 322;
P. A. M. Dirac, Physik Zeits. Sow. 3 (1933) 64;
W. Pauli, Solvey Berichte (1939);
W. Heisenberg and W. Pauli, Z. Phys. 56 (1929) 1;
E. C. G. Stückelberg, Helv. Phys. Acta 11 (1928) 225;
W. Heisenberg, Z. Phys. 110 (1938) 251;
P. A. M. Dirac, Proc. Roy. Soc. A136 (1932) 453;
F. Bloch, Physik Zeits. Sow. 5 (1934) 301;
