We construct an explicit covariant Majorana formulation of Maxwell electromagnetism which does not make use of vector 4-potential. This allows us to write a “Dirac” equation for the photon containing all the known properties of it. In particular, the spin and (intrinsic) boost matrices are derived and the helicity properties of the photon are studied.

This paper presents a case study of the “electric hypothesis” of the causes of earthquakes, which emerged in the second half of the eighteenth century as part of the first studies of seismology. This hypothesis was related to Franklin’s views on atmospheric electricity and developed in a period when electric phenomena were widely studied, and was essentially based on solid empirical evidence and confirmed by model experiments. Even though it resulted from scientific reasoning, the theory remained strongly empirical, and was (...) supported by Italian scholars who were familiar with seismic events. Among these, Giuseppe Saverio Poli, a follower of Franklin, was able to provide a careful and comprehensive explanation of the disastrous earthquake of 1783, which occurred in Calabria, a region of southern Italy, and the St. Anne earthquake of 1805, by drawing not just upon the electric evidence, but all the relevant phenomenology available. We outline here the emergence, the development, and the later evolution (up to the beginning of the nineteenth century) of the “electric earthquake” paradigm by focusing on different works by Poli, including a previously unknown manuscript containing a thorough account of the Calabria earthquake prepared by the Neapolitan scholar for the Royal Society. The present case study therefore offers the opportunity to illustrate how electrical science shaped earthquake science to a degree not usually appreciated in the literature, and is also supported to some extent by the transition from Enlightenment scientific ideals to the Romantic conception of unity in the natural world, in search of common causes among phenomena belonging to different fields. (shrink)

We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.

The two-electron atom is the simplest nontrivial quantum system not amenable to exact solutions. Today, its relevance in the development of quantum mechanics and its pedagogical value within the realm of atomic physics are widely recognized. In this work, an historical review of the known different methods and results devised to study such a problem is presented, with an emphasis to the calculations of the ground state energy of helium. Then we discuss several, related, unpublished results obtained around the same (...) years by Ettore Majorana, which remained unknown till recent times. Among them a general variant of the variational method appears to be particularly interesting, even for current research in atomic and nuclear physics: it takes directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Further relevant contributions, specialized to the two-electron problem, include the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results) and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable. Finally a survey of results, relevant mainly for pedagogical reasons, is given; in particular we focus on simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as on a simple alternative to Hylleraas’ method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas. (shrink)

A complete theoretical model describing artificial disintegration of nuclei by bombardment with α-particles, developed by Majorana as early as 1930, is discussed in detail jointly with the basic experimental evidences that motivated it. By following the quantum dynamics of a state resulting from the superposition of a discrete state with a continuum one, whose interaction is described by a given potential term, Majorana obtained (among the other predictions) the explicit expression for the integrated cross section of the nuclear process, which (...) is the directly measurable quantity of interest in the experiments. Although this is the first application of the concept of quasi-stationary states to a Nuclear Physics problem, it seems also that the unpublished Majorana work anticipates by several years the related seminal paper by Fano on Atomic Physics. (shrink)

This biography sheds new light on the life and work of physicist Ettore Majorana (including unpublished contributions), as well as on his mysterious disappearance in March 1938. Majorana is held by many, including Nobel Laureate, Enrico Fermi, to have been a genius of the rank of Galilei and Newton. In this intriguing story, the author, himself a leading expert on the work of Majorana, supplements the existing literature with new insights, anecdotes and personal accounts of contemporaries of Majorana.

We give an accurate historical and scientific account of a practically 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 English 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 is one of 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. (shrink)

We give an accurate historical and scientific account of a practically 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 English translation. It is likely related to an invited talk for a conference at Leningrad in 1933 which, however, Majorana never attended. Probably this manuscript is one of 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. (shrink)

After a quick historical account of the introduction of the group-theoretical description of quantum mechanics in terms of symmetries, as proposed by Weyl, we examine some unpublished papers by Ettore Majorana. Remarkable results achieved by him in frontier research topics as well as in physics teaching point out that the Italian physicist can be well considered as a follower of Weyl in his reformulation of quantum mechanics.