Connection between the isorotator model of the hot particles and the d’Espagnat-Prentki theory

Abstract

This paper deals with the connection between the screw model of the hot particles in isobaric spin space and the D' Espagnat-Prentkl theory. The theory says nothing about the rest mass of the elementary particle, whlle Rayski's theory leads in a very simple way to the mass quantization, though there are some arbitrary features in his model. It seems expedient to combine the positive properties of these theories. Rayski, however, provides the field quantity of the isorotator with two isospin indices corresponding to the isobaric spins of the two points. Fortunately, it can be shown that the eigenfunctions of the mass operator with respect to the rotations and inversions in isobaric spin space (u- space) transform as the D'Espagnat-Prentki's field quantities. This means a close connection between the two theories. In the proof use is made of the fact that the mass eigenequation must be covariant with respect to the rotations and inversions in u-space, which is very natural from the physical point of view.