The Rotator Theory of Elementary Particles and the Baryon Masses

This paper is dealing with the relativistic rotator theory recently proposed for represent-ting the elementary particles. A comparison is established between the "internal " invariance group which lies at the basis of this theory, and the Dirac spin group used in the "external" treatment. It is shown, in the frame of Yukawa's scheme, that the external group is the connected Dirac group, which can be split into two complexified Pauli groups. In this frame, an internal Hamiltonian can be built. This Hamiltonian yields all observed strong interactions, besides unobserved ones, which would take place with the new unstable baryons introduced by the theory. From this Hamiltonian. the proper energies are derived in the usual way, and this treat~ent yields between the masses of the four known baryon multi-plets a numerical relation which fits in exactly with the experimental data. A "rotator theory " of elementary particles1),~),s) has been proposed, which starts from a classical picture of a particle endowed with a structure extended in space, schematized by an orthonormal relativistic tetrad b/0: b <Ob <~J = 0 b (l;)b C7Jl = (Jh fb V f"V ' fb f