Transformation Properties of the Rigid Sphere Wave Functions and Their Relation to the Dirac Spinor

Abstract

It is shown that the wave functions of a rigid sphere belonging to the eigen­ value J = 1/2, where J denotes the magnitude of the angular momentum due to the rotation of the sphere around its center of mass, transform in exactly the same way as the Dirac spinor under the spatial rotation, space inversion and the Lorentz transformation, and that the Dirac equation is derived automatically from the pro­ perties of these wave functions. the Dirac equation is derived in such a model. In this paper we want to show that the wave functions of a rigid sphere belonging to the eigenvalue J = 1/2, where J denotes the magnitude of the angular momentum due to the rotation of the sphere around its center of mass, transform in exactly the same way as the Dirac spinor under the spatial rotation, space inversion and the Lorentz transformation, and that the Dirac equation is derived automatically from the explicit form of these wave functions.***) We think that this result gives a strong support to the non-point model of elementary particles, since if we give spatial extension to elementary particles, the rotational mode is inherent to them, whatever the form of the extension may be. In §2, we discuss the transformation properties of the wave func­ tions. In §3, the derivation of the Dirac equation is given.