par Schonberg, Mario
Référence Il Nuovo cimento, 10, 6, page (1-48)
Publication Publié, 1953-06
Article révisé par les pairs
Résumé : It is shown that the second quantization methods are a general mathematical technique applicable to formalisms involving linear equations of change, differential with respect to the time variable. The ordinary second quantization formalism for systems of bosons or fermions, and the « second quantization » of the classical theory developed by the author are obtained as particular cases of the general methods. There are several ways of applying the second quantization methods to the same linear problem, which lead to different formalisms. A very simple kind of second quantization is applied to the Schrödinger equation of an arbitrary mechanical system in order to develop a new treatment of the statistical quantum mechanics (the Gibbs second quantization). In this way a straightforward method of intioducing the Gibbs ensembles and grand ensembles is obtained. The entropy is discussed with the Gibbs second quantization. Some ergodic theorems of the genera] second quantization and the quantum mechanics are derived. © 1953 Società Italiana di Fisica.