Hole Theory and Quantum Electrodynamics in an Unknown French Manuscript by Ettore Majorana

We give an accurate historical and scientific account of a previously unknown manuscript written by Ettore Majorana in French. The retrieved text deals with Quantum Electrodynamics by using the formalism of field quantization, and it is here reported, for the first time, in translation. It is likely related to an invited talk for a conference at Leningrad (or Kharkov) in 1933 (or 1934) which, however, Majorana never attended. Probably this manuscript refers to the last missing papers of the “Senatore folder”, given by Majorana to one student of his at the University of Naples in 1938, just before his disappearance. 1. The last papers written by Majorana Ettore Majorana, born on 5 August 1906, taught from January to March 1938 at the University of Naples, having obtained the full professorship in Theoretical Physics “for high and well-deserved fame” [1, 2]. The interest in the course held by the great Italian physicist, the only one effectively delivered to students [3], has been already pointed out in the literature (see, for example, Refs. [4], [5]). It is fundamentally based on the forefront feature with which Majorana characterized his teaching of Quantum Mechanics. The historical and personal adventure of Majorana, instead, is centered around his mysterious disappearance at the end of March 1938, exactly during his stay in Naples. On Friday 25 March (Majorana held his 21st lesson the day before), according to one of his student, ≪contrary to what he usually did, Majorana came to the institute and remained there for few minutes... From the corridor leading to the small room where I was writing, he called me by name: ‘Miss Senatore...’. He didn’t enter in the room but remained in the corridor; I went to him, and he gave me a closed folder, telling me: ‘that’s some papers, some notes, take them.... We will talk about them later’. Afterwards he went away and, turning around, said again, ‘we will talk about them later’.≫ [6]. That folder contained the lecture notes for the course on Theoretical Physics prepared by Majorana who, in that occasion, wanted to give once and for all to one of his student. What remains of the original papers with those notes was published some years ago [7]. However, when Senatore looked at such publication, after very many years since 1938, she pointed out that ≪some chapters of the lectures are missing; their text (completed by the notes of the lecture the professor would have delivered on the day after his disappearance) was given to me. A few other sheets are still missing; these were written in the same original and neat way as the others, but they do not correspond to the lectures he had already given≫ [6]. The path followed by the original notes by Majorana from 1938 to 1966, when Edoardo Amaldi deposited them at the Domus Galilaeana in Pisa together with the other scientific (unpublished) papers