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The onset and the development of the concept of exchange force in quantum physics are historically reconstructed, starting from Heisenberg's seminal contributions in 1926 and going through the great developments in nuclear physics, which allowed the emergence of the idea of force mediating virtual quanta. Although most of such work was performed in Europe, the last and decisive effort in this long path was carried out by Japanese scientists in the 1930s. This is the main focus of the present work, which retraces the achievements of Yukawa and Tomonaga, whose results and mutual interactions are carefully analyzed and related to those of European physicists. [ABSTRACT FROM AUTHOR]