On the transformation properties of strong interactions

Abstract

By extending the procedure outlined in previous papers of grouping several baryon states to form many-component spinors obeying symmetry properties which are not apparent for the separate states, a general Dirac equation satisfied by a 32-component spinor including all the known baryon states is proposed and its properties are discussed. The baryon states, apart from the normal space time co-ordinates, are described by two kinds of independent internal parameters: the isospin variables and the hypercharge variables. The K interactions are expressed by two independent terms with two different interaction constantsF andF′, each of which is invariant for rotations in a 4 dimensional hypercharge space, and the pion interactions by the usual expression invariant for rotations in a 3 dimensional isospin space, quite independent from the hypercharge space; and finally electromagnetic interactions are formulated by the combination of two terms which allow to obtain the experimentally known charge labellings of the different baryon states when a two step separation process is applied to the equation, which leads for the K transitions to selection rules expressing naturally the conservation of hypercharge or strangeness as it is formulated in the doublet approximation. The combination of the two K interaction terms allows further to obtain two kinds of coupling constantsF+F′ andF -F′ for the different interaction terms, disposed in such a way as to explain the observed different self masses of the baryons. It is further shown that the 32-component equation is invariant under boson, spinor and charge conjugation operations separately, which are rigorously valid even when the different baryon masses are included. Finally some aspects of the γ5 transformation properties of the equation are discussed. The present approach seems therefore adequate to unify under few common points-of-view the treatment of the baryon states and to put into evidence some general invariance properties which otherwise should not be revealed.