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The many recent researches into the mysterious disappearance of Ettore Majorana, one of the greatest minds of theoretical physics in the twentieth century, are summarised and discussed in some detail. The fate of the Italian scientist is argued to be intimately related to the final months of his life in Naples, from where he decided to disappear in March 1938. This analysis of accurate and detailed investigations performed in the last few years, together with facts already known, reveals a fascinating and intriguing picture, which was previously unexpected. New light on the disappearance of Majorana, a mystery that has lasted for more than 70 years, then emerges. [ABSTRACT FROM AUTHOR]

Abstract: We present and analyze in detail an unknown theory of ferromagnetism developed by Ettore Majorana as early as the beginnings of 1930s, substantially different in the methods employed from the well-known Heisenberg theory of 1928 (and from later formulations by Bloch and others). Similarly to this, however, it describes successfully the main features of ferromagnetism, although the key equation for the spontaneous mean magnetization and the expression for the Curie temperature are different from those deduced in the Heisenberg theory (and in the original phenomenological Weiss theory). The theory presented here contains also a peculiar prediction for the number of nearest neighbors required to realize ferromagnetism, which avoids the corresponding arbitrary assumption made by Heisenberg on the basis of known (at that time) experimental observations. Some applications of the theory (linear chain, triangular chain, etc.) are, as well, considered. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

An account is given of some topical unpublished work by Ettore Majorana, revealing his very deep intuitions and skillfulness in Theoretical Physics. The relevance of the quite unknown results obtained by him is pointed out as well [ABSTRACT FROM AUTHOR]

We study two celebrated Majorana's papers through a method of investigation which relies upon the recently recognised distinction between classical logic and grosso modo the several kinds of non-classical logics, i.e. the failure of the double negation law. This law fails when a double negated sentence is not equivalent to the corresponding positive sentence, owing to the lack of scientific evidence of the latter one. All recognised double negated sentences inside the text of each paper are listed; the mere sequence of such sentences gives the logical thread of Majorana's arguing. This one is recognised to be of the Lagrangian kind, which mixes logical arguing and mathematical calculation; i.e. the author puts a fundamental problem which is solved by anticipating the mathematical hypothesis which is capable of solving it, and then by drawing from this hypothesis the mathematical consequences in order to obtain the desired result. Furthermore Majorana's rhetoric of presentation results to be a juridical one, owing to his style of presenting the laws to which an ideal theoretical physicist has to conform himself in order to solve the problem at issue. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]