Extended Particle Model of Elementary Particles

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Abstract
A unified model of elementary particles, especially that of hadrons, is discussed based upon an assumption that the elementary particles are mathematical point 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 this structure is rigid. In this case, the internal motion is the rotation around the center of mass, and the internal states are specified by three quantum numbers J, K and M, which specify the magnitude of the angular momentum due to this rotation and its component along the third axis of the body fixed and the laboratory fixed frame, respectively. Clearly, J and M should be interpreted as the magnitude and the third component of the spin, while it is shown that K can be identified with the twice of the baryonic (or leptonic) number. The equation of motion to be satisfied by such a system is a generalization of the Feynman-Gell-Mann equation which is equivalent to the generalized Dirac equation. Further it can be shown that in this model the mirror image of a particle is its antiparticle. Therefore, the invariance of the physical law under the space inversion leads to the conservation of CP rather than the conservation of P. If we allow deformability, the body possesses, in addition to the degree of freedom of the rotation, the degree of freedom of the deformation. It can be shown that in the first approximation in which these deformations are approximated by simple harmonic oscillations near the equilibrium points, the motion of such a system near the ground state can be described in terms of the excitons which describe the rotation and the deformation of the system, in which this deformation is caused by the Coriolis force due to the rotation excited by the excitons. It is shown that as far as the spin and the unitary spin quantum numbers are concerned, these excitons can be identified with the quark and the antiquark. But they obey the Bose statistics and have the rest mass about one third of the nucleon mass and moreover it can be shown that in this model the triality is restricted to zero. Therefore, particles with fractional electric charge or fractional baryonic number do not appear 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. Thus in this model structure constants like spin, baryonic (leptonic) number, unitary spin, …, etc. are introduced as quantum numbers specifying the internal motion, and the non-conservation of parity or the existence of the internal symmetry like SU3 or SU6 appears as rather general features of the extended particles not necessarily depending upon their specific form, and it is concluded that this model, although naive and simple minded, seems to match very well with the essential features of elementary particles, and may be taken as a starting point for their better understanding.

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