Archive of historical materials
Draft: Density Matrix in the Theory of the Positron (Letter to Phys. Rev. )
OU1936-C1 (4 pages) date: April 21, 1936
This is a handwritten draft of the paper that Yukawa submitted as a letter to the American scientific journal, Physical Review. The final manuscript is shown in OU1936-C6. After Dirac formulated the Dirac equation, he predicted the existence of positrons in order to interpret the negative energy solution that emerged as a result of the equation. At that time, Dirac claimed that the vacuum was a state in which all levels of negative energy were populated by electrons. (This theoretical model of the vacuum is known as the “Dirac sea.”) According to his theory, the vacuum contains an infinite number of electrons. Many physicists found it difficult to accept it and they thought there was a flaw somewhere in Dirac’s theory.
In order to solve the above problem, Yukawa prepared the Dirac field of electrons and the Dirac field of positrons and tried to formulate a theory that would not result in infinite charge when the existing relation between the two fields was imposed. In other words, he attempted to contrive a system that would achieve “normal vacuum state” by canceling the infinite charge of the Dirac sea with both the field of electrons and the field of positrons in the negative energy state. Today, we know that the two fields Yukawa introduced are connected by a process called charge conjugation, so only one field needs to be taken into consideration. In retrospect, Yukawa was almost there.
When Yukawa wrote in English the name of the organization he belonged to at the end of the manuscript draft, he wrote “Department of Physics” of Osaka Imperial University and corrected it to “Institute of Physics.” There is no knowing why he made a change in the English translation of the department’s name. In the following year, he indicated the department as “Department of Physics” as he had done before. (Written by Yutaka Hosotani)
