(b. Tokyo, Japan, 31 March 1906; d. Tokyo, 8 July 1979)
Sin-itiro Tomonaga, who shared the 1965 Nobel Prize with Richard P. Feynman and Julian Schwinger for “fundamental work in quantum electrodynamics,” was the son of Hide and Sanjuro Tomonaga. When Sin-itiro was born, his father, Sanjuro, was a professor at Shinshu University in Tokyo. In 1907 he accepted a chair in philosophy at Kyoto Imperial University. From 1909 to 1913 he studied abroad, mostly in Germany, and his family moved to Tokyo to live with relatives. Sin-itiro spent his first year in primary school there; after the family was reunited in 1913, he attended school in Kyoto. He was frequently ill, and in 1918 he missed the first semester of middle school. Hideki Yukawa, who wzs also to become a Nobel laureate in physics, entered th same school one year after Tomonaga; they became classmates as a result of the latter’s illness and continued to be, at the Third High School and at Kyoto Imperial University.
Tomonaga’s reminsicences, “My Teachers, My Friends,” describe his university experience as so distasteful that he became pessimistic about his future. About the instruction he said, “I thought the level of the lectures was low and was greatly disappointed as I had high expectations, especially for physics.”
Tomonaga’s interest in physics had been stimulated by a well-publicized visit to Japan by Albert Einstein in 1922 and by reading a book on relativity theory by Jun Ishiwara. In high school Niels Bohr’s atomic theory had been discussed, with stress on its abstruse and revolutionary character. Tomonaga’s last year at high school was 1925–1926, the year of the new quantum mechanics of Werner Heisenberg, Erwin Schrödinger, and Paul A. M. Dirac. His physics teacher, Takeo Hori, who had just graduated from Kyoto Imperial University, presented material on matrix mechanics and wave mechanics.
Tomonaga was therefore disappointed with the old-fashioned physics being taught at the university. The theory lectures were tedious and had too many dry formulas; the laboratories were dark, dirty, and old-fashioned. He did, however, find the mathematics instruction interesting and challenging; the instructors were active in research and conveyed their own excitement to the students.
During their final year at the university (1928–1929), Tomonaga, Yukawa, and several other ambitious students studied quantum mechanics together from original journal articles and without a professor. After graduation Tomonaga and Yukawa stayed on in Kyoto as unpaid assistants to Kajuro Tamaki.
In September 1929, Heisenberg and Dirac came to Japan from America, where they had spent the summer, at the invitation of Yoshio Nishina. Tomonaga went to Tokyo to hear their lectures, given in English (published two years later in Japanese). The visitors spoke on their own latest works: Heisenberg on ferromagnetism and Dirac on his relativistic electron theory. Tomonaga was deeply impressed but, being shy, took a rear seat at the lectures and did not meet Nishina or either of the visitors.
However, in 1931 Nishina lectured at Kyoto for a month, and Tomonaga established a good rapport with him. Nishina had returned to Japan in December 1928, after seven years of study in Europe, six of them at Bohr’s institute in Copenhagen, where he had done important theoretical research with Oskar Klein. In Tokyo, at the Institute for Physical and Chemical Research (Riken), the organization he had joined in 1918 and that had financed his stay abroad, Nishina formed a group to do research in both theoretical and experimental nuclear physics. Nishina’s lectures at Kyoto conveyed to Tomonaga and Yukawa the sprit of the Copenhagen approach to quantum mechanics.
Tomonaga joined Nishina’s laboratory at Riken in April 1932 to do theoretical research and began a fruitful scientific collaboration with Nishina. His first five papers, through 1935, are on the creation and annihilation of positrons, and the sixth is on the neutron-proton interaction; all have Nishina as coauther. Other collaborators of his period were H. Tamaki and two of Yukawa’s students from Kyoto, Shoichi Sakata and Minoru Kobayashi.
In the summer of 1933, Nishina, Sakata, and Tomonaga worked together at Gotemba, near Mt. Fuji. Two years later Kobayashi, Tamaki, and Tomonaga rented a villa in Karuizawa. Nagano Prefecture, and translated Dirac’s Principles of Quantum Mechanics into Japanese. A 1935 paper with Nishina and Kobayashi, “On the Creation of Positive and Negative Electrons by Heavy Charged Particles,” is a comprehensive work that complements theoretical studies of this problem by E. J. Williams, J. R. Oppenheimer, L. Landau and E. Lifshitz, E. C. G. Stueckelberg, and other well-known physicists.
Tomonaga’s next three papers, dealing with nuclear structure, are in German. An English paper of 1937 (with Tamaki) treats, for the first time, the collision of a very-high-energy neutrino with a neutron. It is an outgrowth of Heisenberg’s discussion of “explosive showers” produced by cosmic rays and emphasizes the rapid rise, with increased energy, of the probability of neutrino interaction. According to Rudolf Peierls, it “foreshadowed the present role of high-energy neutrinos as practical projectiles.”
At the end of 1937, Tomonaga went to Leipzig to work with Heisenberg and remained there until just before the outbreak of war in Europe in 1939. On his arrival, he found there was a great interest in Yukawa’s meson theory, which attracted worldwide attention at this time because of his discovery of the cosmic-ray meson in 1937, but Heisenberg suggested to Tomonga that he should work first on a less speculative subject. In fact, Tomonaga wanted to improve the compound nucleus model advanced by Bohr in 1936 and 1937. In that model, a nuclear collision results in an excited nucleus (regarded as analogous to a drop of liquid), which then evaporates one or more nucleons. Tomonaga’s idea was to treat the nuclear matter as a degenerate Femi gas and to study the process by which it reaches its equilibrium temperature, taking into account its viscosity and thermal conductivity. His paper was published in Zeitschrift für Physik, and he submitted it to Tokyo Imperial University in 1939 to obtain the D.Sc. degree.
In an interview in 1978, Tomonaga recalled his second research project in Leipzig: to modify Yukawa’s picture of meson decay. It was occasioned by an analysis of cosmic-ray data by Heisenberg and Hans Euler that showed an unexpectedly long mean life of the cosmic-ray meson. Yukawa had postulated a direct decay into an electron and a neutrino, but Tomonaga’s model had the meson decaying (virtually) into a nucleon pair, which was then annihilated to produce the electron and neutrino through the four-fermion beta-decay interaction. The calculation led to an integral that was infinite.
Heisenberg agreed with Tomonaga’s negative conclusion and stated that the perturbation techniques that had yielded useful results for electromagnetic and weak interactions (in spite of difficulties of principle) would be totally inapplicable in meson theory. He handed Tomonaga proof sheets of a paper containing a semiclassical approach to meson interaction, and Tomonaga decided that he would produce a quantum theoretical version of it.
Tomongaga wanted to extend his stay in Leipzig but was dissuaded by the threat of war in Europe. In mid August 1939, Yukawa visited Tomonaga in Leipzig. He was making his first trip out of Japan, having been invited to attend the Eighth Solvay Conference at Brussels in October (later canceled because of the outbreak of war in September) and to lecture to the German Physical Society, which was to meet in September. However, on 25 August they were urgently advised by the Japanese embassy in Berlin to proceed to Hamburg and to board the ship Yasukuni Maru.
The ship took them first to Bergen, Norway, and then to New York, where they visited the World’s Fair. Yukawa traveled overland to the West Coast, while Tomonaga, happy to be in a Japanese setting, remained on the ship as it passed through the Panama Canal, stopped in San Francisco, and continued to Japan.
On 27 October 1940, Tomonaga married Ryoko Sekiguchi, daughter of Kolkichi Sekiguchi, director of the Tokyo Astronomical Observatory and a professor at Tokyo Imperial University; they had three children. He continued his association with Riken, and in 1941 was also appointed professor at Tokyo Bunrika Daigaku (Tokyo University of Literature and Science, which became Tokyo University of Education in 1949, and University of Tsukuba in 1973). In 1944 he became part-time lecturer at Tokyo Imperial University and was also required to do research for the navy.
Like Schwinger, with whom he shared the Nobel Prize, Tomonaga did war work on the theory of microwave circuits and wave guides, especially on the theory of the magnetron oscillator used to generate short radio waves for radar. In a sense, the work was pure engineering, but the physicist’s approach, starting from first principles and applying techniques such as that of the “scattering matrix” used in nuclear physics (a theory extended by Heisenberg in the 1940’s) proved to be very powerful. With Masao Kotani, Tomonaga was awarded the Japan Academy Prize in 1948 for his work on the magnetron.
Aside from military research, Tomonaga’s work in the 1940’s was mainly on the theory of mesons and on quantum electrodynamics, with many of his ideas stemming from what he had done at Leipzig. The first work he did after returning from Germany led to his writing a letter of Physical Review with Gentaro Araki that emphasized the differences between the nuclear capture rates of slow positive and negative mesons. They pointed out that “the competition between nuclear capture rates and spontaneous disintegration must in this way be different for mesons of different gigns”. Checking of the Tomonaga-Araki predictions by the Rome group of M. Conversi, E. Pancini, and O. Piccioni, in experiments begun in 1943 and completed in 1946, showed conclusively that the cosmic-ray meson observed at sea level could not be the Yukawa nuclear-force meson, because it interacted only weakly with nucleons.
A second line of research led to a unique “intermediate coupling” approximation for meson theory. The strength of an elementary electromagnetic interaction (between, say, an electron and a photon) is measured by a dimensionless quantity called the fine-structure constant. It is equal to the square of the electron’s charge multiplied by 2π and divided by the product of Planck’s constant and the velocity of light, its value being about 1/137. The analogous quantity in the meson theory, obtained by substituting the meson “coupling constant” g for the electronic charge e, has a value near I. Consequently, the method usually used to obtain results in quantum electrodynamics—the expansion of the interaction probability in powers of the fine-structure constant (the so-called perturbation method)—cannot be used effectively in meson theory.
In 1940, Gregor Wentzel at Zurich introduced the “strong-coupling” approximation, in which an expansion is made in powers of the inverse of the coupling constant. Wentzel’s treatment gave new predictions not obtainable by perturbation theory, such as strongly bound states of the nucleon with one or more mesons (isobars). In his paper of 1941, “Zur Theorie des Mesons, I”, Tomonaga points out that the meson coupling is effectively near unity, so that one anticipates a “poor convergence for both [that is, strong and weak coupling] approximation.” Thus a third procedure is called for, one that is useful for an intermediate coupling.
The method invented by Tomonaga and developed in a series of papers (some with Tatsuoki Miyazima and others) resembles the so-called Hartree approximation, often used in the treatment of multiparticle systems such as atoms or nuclei, but differs from it in that the number of particles (mesons) is not fixed.
Unquestionably, though, the most important work of Tomonaga is based upon his paper “On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields”, The English version, in the first issue of Progress of Theoretical Physics, a journal that Yukawa started in 1946, is a translation of a paper that appeared in 1943 in the Riken journal (Riken-iho).
Tomonaga’s paper is a generalization to quantum field theory of a prophetic work by Dirac, done in 1932, in which each of a set of particles carries its own time variable as well as a spatial label, Dirac’s “many-time” thèory. The equal treatment of time and space, in contrast with the usual Hamiltonian treatment that singles out the time variable, makes possible a fully relativistic treatment of the many-particle problem. Tomonaga’s Nobel address begins by discussing his generalization of Dirac’s theory to an infinite number of degrees of freedom (that is, to a quantum field), the usper-many-time theory; “This paper of Dirac’s attracted my interest because of the novelty of its philosophy and the beauty of its form.”
The essential point was the description of the field on a succession of arbitrary spacelike surfaces. As Julian Schwinger put it in 1980:
All of space at a common time is but a particular coordinate description of a plane spacelike surface. Therefore the Schrödinger equation, in which time advanced by a common amount everywhere in space, should be regarded as describing the normal displacement of a plane spacelike surface. Its immediate generalization is to the change from one arbitrary spacelike surface to an infinitesimally neighboring one, which change can be localized in the neighborhood of a given space-time point. Such is the nature of the generalized Schrödinger equation that Tomonaga constructed in 1943, and to which I came toward the end of 1947 (Birth of particle Physics, p. 364).
Because of the intense bombing of Tokyo, in April 1944 Tomonaga sent his family to live in the country while he remained in the city. By September several physicists without their families were sharing his house. He went sometimes to the Shimada Naval Research Laboratory to work on radar. However, Tomonaga’s health became bad once again, and in December he was obliged to take to bed on account of eye trouble and infected teeth. On 13 April 1945, the area of professors’ houses near Tokyo University was completely burned out, including the houses of Tomonaga and Nishina, as was Riken.
During this period Satio Hayakawa kept a notebook that he used in writing an article (1988) that describes Tomonaga as “a great teacher”, Released from military service in November 1944, he had returned to the University of Tokyo and, together with fellow students Hiroshi Fukuda, Ziro Koba, and Yoneji Miyamoto, enrolled in a seminar course taught by Tomonaga. All of them, as well as Takao Tati, Daisuke Ito, and Suteo Kanesawa, were subsequently coauthors with Tomonaga of one or more of the nearly tow dozen papers on cosmic-ray phenomena, quantum theory, and renormalization theory that he wrote during the next few years.
In April 1946 Tomonaga described to the students his ambitious program: to develop a completely covariant quantum electrodynamics to the point where it could be applied to realistic problems. First it would be necessary to modify the so-called auxiliary (or subsidiary) condition that is imposed on the four-vector potential in the classical Hamiltonian theory of the electromagnetic field to obtain Maxwell’s equations. The analogous procedure in the quantum field theory results in the separation of the instantaneous Cooulomb interaction from the retarded transverse radiation field. While that is convenient for treating many problems. It destroys the relativistic covariance of the theory.
Once a covariant formulation for the electromagnetic field had been obtained, it was combined with Dirac’s electron theory and tested by solving problems in the framework of many-time theory. Then they turned to Tomonaga’s more general super-many-time theory and applied it to the electomagnetic interactions of electrons, did the same for mesons, and then attacked the meson-nucleon interaction.
By 1 July 1946 the formulation of quantum electrodynamics in super-many -time theory was nearly completed, with Koba, Hayakawa, and Miyamoto doing significant work; then, with Kanesawa, Tomonaga began to consider the electromagnetic interactions of the vector meson. By early August, Tomonaga decided it was time to prepare a series of papers for publication. The whole group would contribute to these, with authorship assigned to subsets of the members in a somewhat arbitrary manner. At a meeting of the Physical Society at Kyoto University on 21 and 22 November 1946, no fewer than twenty-three papers were presented by Tomonaga and his associates.
At the same meeting, Sakata presented a theory of mixed fields, which, as he and Osamu Hara showed, gave no electromagnetic self-energy correction to the mass of the electron; in the standard theory, the result was infinity. Sakata’s theory was similar to one proposed by Fritz Bopp in Germany, which canceled the electromagnetic self–energy of the electron by assuming that this particle also interacted with a neutral vector field of negative energy. The Sakata-Hara work replaced Bopp’s vector field with a neutral scalar meson field, with positive energy, and accordingly could be considered “realistic” rather than a mathematical artifice. Sakata called the scalar field that stabilized the electron the “Cohesive field” and named its quantum the C-meson. Tomonaga, struck by Sakata’s suggestion, wondered whether the removal of the self-energy divergence would work in a higher order of approximation.
In 1947 the Tomonaga group began to recalculate the radiative corrections to the elastic scattering of an electron in a Coulomb field (calculated in 1939 by Sydney M. Dancoff in the United States), using the idea of the cohesive field. At first their result was negative; an infinite term appeared in the scattering probability (in addition to another infinity, due to the polarization of the vacuum, against which the cohesive field was known to be powerless). However, in the course of the calculation Tomonaga developed a new calculational method, much more transperent, and with its aid they discovered an error in Dancoff’s work; the final answer was then finite. Dancoff had introduced the word “renormalization” and had tried to express the infinities in the scattering problem in terms of mass and charge renormalization; except for his calculational error, he would have succeeded.
Renormalization means a redefinition of the theoretical mass and charge of the electorn, which are inserted at the starting point of the theory of quantum electrodynamics as “bare” nonphysical quantities. The observable mass and charge are defined to be sum of the “bare” quantities and their radiative corrections (which involve the virtual creation and annihilation of photons and electron-position pairs). Stated thus, the idea may appear self-evident, but since the “corrections” are infinite and of opposite sign. The scheme thus involves a delicate mathematical cancellation.
Communication with the West was still a problem in Japan, but gradually news filtered through that similar developments were taking place in the United States. On 26 April 1947, Willis E. Lamb, Jr. and Robert C. Retherford discovered an anomaly in the hydrogen spectrum. Lamb reported it in June at a small private conference on Shelter Island, New York, attended by both Feynman and Schwinger. Soon afterward, Hans Bethe explained the main part of the effect by a nonrelativistic application of the renormalization method. Tomonaga read about these exciting developments in Time and Newsweek.
The shift of energy separating the first and second excited levels of the hydrogen atom, the Lamb shift, was the first testing ground of the new quantum electrodynamics, which was rapidly applied to extend Bethe’s calculation to the relativistic region. Besides the calculations of Feynman and Schwinger, of Tomonaga (with fukuda and Miyamoto), and of Lamb (with Norman M. Knoll), the same calculations were independently done by J. Bruce French and Victor F. Weisskopf and by Yoichiro Nambu.
In the years 1948 and 1949 Yukawa was at the Institute for Advanced Study in Princeton, after which he accepted a chair at Columbia University (1949–1953). His letters to colleagues in Japan helped to keep them in touch with developments in the West. In the years 1949 to 1950 Tomonaga was a member of the Institute for Advanced Study, and he wrote letters that were published in the informal journal Soryushiron Kenkyu. At Princeton he worked on the properties of nuclear matter.
After his return to Japan in 1950, Tomonaga continued to do physics research but was increasingly involved in scientific administration, becoming a member (later president) of the Science Council of Japan, succeeding Nishina in 1951. In 1956 he was elected president of Tokyo University of Education. From 1957 on, he was active in movements against the deployment of nuclear weapons, such as the Pugwash conferences.
Besides the Nobel Prize (1965) and the Japan Academy Prize (1948), Tomonaga received numerous other honors. They included Japan’s highest award, the Cultural Medal (1952) and the Lomonosov Medal of the Academy of Sciences of the U.S.S.R. (1964). He was a member of the Japan Academy, the Royal Swedish Academy of Sciences, the (U.S.) National Academy of Sciences, and the American Philosophical Society.
I. Original Works. Most of Tomonaga’s original scientific work is in his Scientific Papers of Tomonaga, T. Miyazima, ed., 2 vols. (Tokyo, 1971–1976). Volume I contains the physics papers, in English and German, and Tomonaga’s Nobel lecture. Volume II contains articles on ultrashort wave circuits and the magnetron, review articles in Japanese on nuclear and elementary particle physics, and letters written from America to Japanese colleagues. Tomonaga’s textbook Quantum Mechanics, Masatoshi Koshiba, trans., 2 vols. (Amsterdam, 1962–1966), has a historical plan. Eighteen volumes of his essays, letters, and diaries have been published in Japanese. His papers are at Riken (Tokyo) and at Tsukuba University.
II. Secondary Literature. Several articles on Japanese elementary panicle physics are in Shigeru Naka-yama. David L. Swain, and Eri Yagi, eds., Science and Society in Modern Japan (Cambridge, Mass., 1974). “Nuclear Research at Riken,” a “dialogue” with Tomonaga, is in L. M. Brown, M. Konuma, and Z. Maid, eds.. Particle Physics in Japan, 1930–1950, II (Kyoto, 1980). See also Julian Schwinger. “Two Shakers of Physics: Memorial Lecture for Sin-itiro Tomonaga,” in Laurie M. Brown and Lillian Hoddeson, eds. The Birth of Particle Physics (Cambridge, 1983), 354–375. A group of papers on Tomonaga (including Satto Hayakawa’s) is in L. M. Brown, R. Kawabe, M. Konuma, and Z. Maki, eds.. Proceedings of the Japan-USA Collaborative Workshops on the History of Particle Theory in Japan, 1935–1960 (Kyoto, 1988), 43–84.
Laurie M. Brown
"Tomonaga, Sin-Itiro." Complete Dictionary of Scientific Biography. . Encyclopedia.com. (January 20, 2018). http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/tomonaga-sin-itiro
"Tomonaga, Sin-Itiro." Complete Dictionary of Scientific Biography. . Retrieved January 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/tomonaga-sin-itiro
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
The Japanese physicist Sin-itiro Tomonaga (1906-1979) is best known for his fundamental contributions to quantum electrodynamics.
The oldest son of a philosopher and university professor, Sin-itiro Tomonaga was born on March 31, 1906, in Tokyo. After obtaining his degree from Kyoto University in 1929, he spent 3 years as a research student in Kajuro Tomaki's laboratory at the university and then became a research student under Yoshio Nishina in the Science Research Institute in Tokyo. Tomonaga remained there until 1940, with the exception of some time spent in 1939 at the University of Leipzig with Werner Heisenberg.
In 1940 Tomonaga married Rijo, by whom he had three children. In 1941, he became professor of physics at the Tokyo University of Science and Literature (which after the war became part of the Tokyo University of Education).
During the war years, while working in complete isolation from other physicists, Tomonaga made the contributions to quantum electrodynamics for which he shared the Nobel Prize of 1965 with Julian Schwinger of Harvard University and Richard Feynman of the California Institute of Technology. The achievement of these physicists must be understood in the context of the general development of physics since 1925-1926, when quantum mechanics was discovered and elaborated by Heisenberg, Erwin Schrödinger, Paul Dirac, Max Born, and others. Although this elegant theory had been developed specifically to understand the structure of the atom, it was soon generalized by Heisenberg, Wolfgang Pauli, Dirac, and Enrico Fermi to include an explanation of radiation processes and of processes, like the Compton effect, involving the interaction of radiation and matter. The resulting theory—quantum electrodynamics—agreed qualitatively with experiment but refused to yield precise agreement. Most physicists of the 1930s took this to mean that there was something fundamentally wrong with the theory. "Tomonaga, Schwinger, and Feynman, " wrote F. J. Dyson in Science (1965), "rescued the theory without making any radical innovations. Their victory was a victory of conservation. They kept the physical basis of the theory [the postulation of only electrons, positrons, and photons] precisely as it had been laid down by Dirac, and only changed the mathematical superstructure. By polishing and refining with great skill the mathematical formalism, they were able to show that the theory does in fact give meaningful predictions for all observable quantities."
The remarkable thing, as Dyson pointed out, was that, although certain experiments had played a decisive role in Schwinger's and Feynman's thinking, Tomonaga had reached an essentially identical insight on the basis of theoretical considerations alone. He had published those conclusions in Japanese in 1943, but his papers were not translated into English until 1948—until Schwinger and Feynman had been able to direct their efforts away from war-related researches and had independently achieved essentially the same results.
After the war Tomonaga received many honors for his work. Besides the 1965 Nobel Prize, he received the Japan Academy Prize in 1948, the Order of Culture (Japan) in 1952, and the Lomonosov Medal from the USSR in 1964. He was professor of physics at Tokyo University of Education from 1949 to 1969, and served as president of the institution from 1956 until 1962. In 1963, he became director of the university's Institute of Optical Research. He was also president of the Science Council of Japan from 1963 to 1969. He retired from the Tokyo University of Education in 1969, and served as Professor Emeritus until his death in Tokyo on July 8, 1979.
The Nobel Foundation's annual volume Les Prix Nobel 1965 (1966) has, in English, a brief biography of Tomonaga and his personal recollections of the development of quantum electrodynamics. Some background material is in Henry A. Boorse and Lloyd Motz, eds., The World of the Atom (2 vols., 1966). □
"Sin-itiro Tomonaga." Encyclopedia of World Biography. . Encyclopedia.com. (January 20, 2018). http://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/sin-itiro-tomonaga
"Sin-itiro Tomonaga." Encyclopedia of World Biography. . Retrieved January 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/sin-itiro-tomonaga