This was our prediction. Yukawa, Kagaku Tokyo , 12 As a matter of fact, electrons were also treated as waves in the Heisenberg-Pauli theory, and it was well known that this wave treatment was frequently more convenient than the particle treatment. As Dirac already pointed out, the Heisenberg-Pauli theory is built upon the Hamiltonian formalism and therefore the probability amplitude contains only one time variable. This page was last edited on 31 August , at Fukuda, Miyamoto and Tomonaga, Progr. I thought however, that it might be possible without introducing such a drastic change as Yukawa and Dirac tried to do to remedy the unsatisfactory, unpleasant aspect of the Heisenberg-Pauli theory of having a common time at different space points.
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According to him, the quantum-mechanical electromagnetic mass turned out to be infinite, and although the order of the divergence was much weaker than in the case of the Lorentz theory, the observed mass, which included this additional mass, would be infinite. The concept of the electromagnetic mass had already appeared in the classical theory of the electron by Lorentz, who computed the electromagnetic mass by applying the classical theory and obtained the result that the mass becomes infinite for the point zero size electron.
Let us consider, as a concrete example, a problem in which an electron is scattered by an external field. At the same time I happened to discover a simpler method of calculation. During the war he studied the magnetronmeson theory, and his super-many-time theory. This was our prediction.
Similarly, I tried in quantum field theory to see whether it was possible to assign different times, instead of one common time, to each space point.
Heisenberg 14in his paper published inemphasized that the field reaction would be crucial in meson-nucleon scattering. Tomonaga applied his super-many-time theory and a relativistic method based on the non-relativistic method of Wolfgang Pauli and Fierz to greatly speed up and clarify the calculations. Inwhile working at Leipzig University Leipzighe collaborated with the research group of Werner Heisenberg. In turn, this field, the so-called self-field of the electron, interacts with the electron.
Van der Waals Just at that time I was studying at Leipzig, and I still remember vividly how Heisenberg enthusiastically explained this idea to me and handed me galley proofs of his forthcoming paper.
This would be, of course, contrary to experiment. In particular, little by little news arrived that the so-called Lamb-shift was discovered 22 as a manifestation of the electromagnetic field reaction and that Bethe 23 was calculating it theoretically.
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In particular, infinite quantities always arise which are associated with the presence of field reactions in various processes. What was understood from these models, was that the most strongly divergent terms in the scattering process had the same form as the expression giving the modification of the particle mass due to field reactions, and therefore both should be manifestations of the same effect. Based on such a philosophy, Dirac proposed a new theory, the so-called many-time theory, which, besides being a concrete example of his philosophy was of much more satisfactory and beautiful form than other theories presented up to then.
During graduate school at the same university, he worked as an assistant in the university for three years. The first information concerning the Lamb-shift was obtained not through the Physical Reviewbut through the popular science column of a weekly U. The conclusions of these people were fatal to the theory.
The Hamiltonian dynamics was developed on the basis of non-relativistic concepts which make a sharp distinction between time and space. Kyoto3 ; Tati and Tomonaga, ibid. Since this is so, and particularly since the theory is unable to calculate the modified mass and charge, we may adopt the procedure of substituting experimental values for them phenomenologically. In this paper, he discussed the formulation of relativistic quantum mechanics, especially that of electrons interacting with the electromagnetic field.
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Select the category or categories you would like to filter by Physics. Furthermore, Feynman 26 devised a convenient method based on an ingenious idea which could be used to extend the approximation of Schwinger and ours to higher orders, and Dyson 27 showed that all infinities appearing in quantum electrodynamics could be treated by the renormalization procedure to an arbitrarily high order of approximation.
In other words, at least a portion of the infinities appearing in the scattering process could be amalgamated into the infinity associated with the particle mass, leaving infinities proper to the scattering process alone.
Quantum mechanics – Shinʼichirō Tomonaga – Google Books
I found out immediately however, without performing the calculation through to the end, that it would yield the same answer as the previous theory. These turned out to be more weakly divergent than the infinity associated with the mass. This was first discussed by Bloch 5 in