Rigid Sphere Model of Elementary Particles and the Electromagnetic Field

Abstract

As is well known, the isospin has been introduced in an intimate relation with the electromagnetic field. An attempt is made to derive this relation based upon the rigid sphere model of elementary particles, starting from the five dimensional theory proposed by Kaluza and Klein. The field equation for the metric field is given uniquely by the requirement of general covariance. In the first approximation with respect to the square root of the gravitational constant, this equation reduces to Maxwell's equation with Q=eI3, where Q is the electric charge and I3 is the third componet of the isospin given by Nakano, Takabayasi and Vigier in their theories of the extended particle model of elementary particles. The fact that the electromagnetic field defines a special direction in the isospace follows very naturally from this field equation. Thus, in our approach all characteristic features of the electromagnetic field as well as the relation between the electromagnetic field and the isospin are derived as a necessary consequence of the theory, without any furthere specific assumptions.