# Tomonaga, Sin-Itiro

# TOMONAGA, SIN-ITIRO

The Japanese theoretical physicist Sin-itiro Tomonaga, who shared the 1965 Nobel Prize in Physics with Richard P. Feynman and Julian Schwinger, was born in Tokyo on March 31, 1906, the son of Hide and Sanjuro Tomonaga. A professor of philosophy at Shinshu University, Sanjuro moved in 1907 to Kyoto Imperial University, and it was in Kyoto that Sin-itiro was educated.

## Undergraduate and Postgraduate Work and Early Research

At Kyoto Imperial University Tomonaga and his classmate Hideki Yukawa (who later won a Nobel Prize in Physics for his meson theory of nuclear forces) studied quantum mechanics from the original physics articles which arrived from abroad during the critical years 1926–1929. After graduation, both budding physicists stayed at Kyoto for several additional years of research. In April 1932, Tomonaga joined the Tokyo group of Yoshio Nishina, Japan's leading nuclear physicist. Nishina, who had worked in Europe for eight years, returned in 1928 to establish a laboratory of nuclear physics at the Institute for Physical and Chemical Research (Riken) in Tokyo, the organization which had financed his stay abroad.

Working with Nishina, Tomonaga did theoretical research on the annihilation of positrons, on the nature of the neutron-proton force, and on the probability of collision of a high-energy neutrino with a neutron. At the end of 1937, Tomonaga traveled to Leipzig, Germany, where he worked with Werner Heisenberg until the outbreak of World War II in 1939.

Heisenberg suggested that Tomonaga work on improving Bohr's theory of the compound nucleus. In that theory, a nucleus struck by a high-energy particle behaves like a drop of liquid. The nucleus "heats up" and evaporates one or more nuclear particles. Tomonaga published his study in a German journal and also submitted it as a thesis to Tokyo Imperial University; he received the degree of D.Sc. in 1939.

As his second research project in Leipzig, Tomonaga worked on the properties of recently discovered cosmic-ray particles, which resembled the mesons proposed by Yukawa. The theory predicted that these new particles should decay to an electron and a neutrino, but the observed mean lifetime for decay was about one hundred times too long. Tomonaga's model, using quantum field theory, led to a result that was infinite. Such infinite predictions had also appeared in quantum electrodynamics (QED), and this Leipzig experience eventually led Tomonaga to his Nobel Prize.

## Research during the Second World War

In mid-August 1939, Yukawa visited Tomonaga in Leipzig on his first trip abroad, where he was invited to speak at several European conferences. However, on August 25, 1939, both physicists were advised by the Japanese Embassy in Berlin to return to Japan because of the impending outbreak of war in Europe. War broke out on September 1, the same day that they began their homeward voyage via the Panama Canal.

Tomonaga continued his association at Riken and also became professor at the Tokyo University of Science and Literature (which later became Tokyo University of Education and, in 1973, the University of Tsukuba). After Pearl Harbor, he did military research for the Japanese Navy on the theory of microwave circuits and waveguides related to radar. Especially, he worked out the theory, from first principles, of the magnetron, an oscillator to generate powerful microwaves. In this work, he applied mathematical techniques that had originated in the earlier study of nuclear collisions. With Masao Kotani, Tomonaga received the Japan Academy Prize in 1949 for this research.

Aside from his war work, Tomonaga made important contributions during this period to quantum field theories, both mesons and QED. The approach to QED involved an approximation called perturbation theory, which was an expansion of the various probabilities for scattering, absorption, etc., in powers of the so-called fine structure constant, whose value is approximately 1/137. However, expansion terms beyond the first generally gave the absurd result infinity, unless an arbitrary cutoff procedure was adopted.

The situation in meson theory was even worse, as perturbation theory failed, even with cutoffs. The reason was that the analogue of the fine structure constant in meson theory was close to unity. Tomonaga, and some collaborators, developed and applied an intermediate coupling approximation, which worked for both strong and weak coupling as well.

## Quantum Electrodynamics

Tomonaga's most important paper, written in 1943, is called "On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields." It is a generalization of a 1932 work of Dirac, in which each of a set of electrons (or other elementary particles) carries its own time variable, Dirac's many-time theory. Treating time and space on an equal footing, this makes possible a fully relativistic treatment of many particles in interaction. Tomonaga generalized this to quantum field theory, with its infinite number of degrees of freedom—his so-called super-many-time theory. Effectively, the field is described on a succession of arbitrarily chosen space-like surfaces (curved in four dimensions), taking the place of "flat" planes of constant time.

Almost the same point of view was taken independently by Schwinger(several years later). Both theorists used this new approach to treat problems in QED, especially allowing them to carry out a procedure known as renormalization, which gave finite, sensible, and it turned out, extremely accurate answers to outstanding problems in QED.

In April 1947, Willis E. Lamb Jr. and Robert C. Retherford discovered an unexpected feature of the spectrum of the hydrogen atom (now called the Lamb Shift) and reported it at a small private conference organized by J. Robert Oppenheimer. In attendance were Schwinger, Feynman, Hans A. Bethe, and Victor F. Weisskopf, all of whom contributed to calculating the Lamb Shift. Tomonaga heard about this and similar effects that experiment had turned up by reading American news magazines. That was sufficient stimulus for the Tokyo group to apply Tomonaga's methods to calculate these effects.

During 1949–1950, Tomonaga was a Member of the Institute for Advanced Study in Princeton, New Jersey. He became president of the Tokyo University of Education in 1956. Besides the 1965 Nobel Prize in Physics, he received other international honors. He died in Tokyo on July 8, 1979.

*See also:*Feyman, Richard; Quantum Electrodynamics; Quantum Field Theory; Schwinger, Julian

## Bibliography

Brown, L. M.; Kawabe, R.; Konuma, M.; and Maki, Z.; eds. "Elementary Particle Theory in Japan. 1930–1960." *Progress of Theoretical Physics Supplement***105** (1991).

Matsui, M., and Ezawa, H. *Sin-itiro Tomonaga—Life of a Japanese Physicist* (MYU Publishing Company, Tokyo, Japan, 1995).

Schwinger, J. "Two Shakers of Physics: Memorial Lecture for Sin-itiro Tomonaga" in *The Birth of Particle Physics,* edited by L. M. Brown and L. Hoddeson (Cambridge University Press, Cambridge, U.K., 1983).

Tomonaga, S. "Development of Quantum Electrodynamics: Personal Recollections." *Physics Today***19** (9), 25–32 (1966).

Tomonaga, S. *Quantum Mechanics: Volume 1. Old Quantum Theory,* translated by M. Koshiba (Interscience, New York,1962).

Tomonaga, S. *Quantum Mechanics: Volume 2. New Quantum Theory,* translated by M. Koshiba (Interscience, New York,1966).

Tomonaga, S. *The Story of Spin,* translated by T. Oka (University of Chicago Press, Chicago, IL, 1997).

*Laurie M. Brown*

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