Deformable Sphere Model of Elementary Particles and its Relation to Quark

Abstract

tion .of the system. As far as the spin and the unitary spin quantum numbers are concerned, these excitons can be identified with the quark and the antiquark. In contrast to the conventional quark, however, they ohey the Bose-statistics and have mass about one third of the nucleon mass. Further in this model it can be shown that the triality is restricted to zero. Therefore, particles with fractional electric charge or fractional baryonic number do not appear. Thus, this model eliminates most of the difficulties of the conventional quark model, and it is shown that as far as the low lying levels of the hadrons are concerned, the elementary particles can be understood consistently as the excited state of a deformable sphere. Discussions in this paper are restricted to the l1niform deformations and is done in the non-relativistic approximation. l ) to construct a unified model of elementary particles on the basis of the assumption that the elementary par­ ticles are' not mathematical points but have some spatial extension, trying to identify the internal levels of motion carried by this extended structure with the actual elementary particles. The simplest possibility for such an approach is to assume that tbis struc­ ture is rigid. In this case, the internal motion is the rotation around 1 he center of mass, and in our previolls paper2) this was shown that the eigenfunctions of the system belonging to the eigenstate of this rotational motion have properties very similar to the Dirac spin or. **) The body model is, however, insufficient as the realistic model of elementary particles, since it has no possibility of producing quantum numbers like isospin, hypercharge,··· etc. To· evade this difficulty, 1\vo of the authors (0. H. and T. G.) have tried to relax the condition rigid , and considered a deformable body model instead of the body