THEORY OF INFINITELY EXTENDED PARTICLES

M. Hessaby, University of Tehran

I. - INTRODUCTION.

The charge density is spread out over all space and the integrals of the charge density and energy density are respectively equal to the charge and mass of the particle. The electric potential thus obtained is inserted in Diary's wave equation, and gives a sales of equations of increasing degree, the first of which gives the mass of the muon.In addition to the expressions obtained for the electric and gravitational potentials, an expression is found for a potential which has the form of a dipole potential.
The difficulties with which the concept of point-like particles is beset, such as the infinities encountered in the existing theories of elementary particles, suggest a different approach to the study of these particles. Instead of restricting ourselves to the concept of point-like particles, we should extend our investigation to the implications of the concept of particles having infinite extension. Such a particle should consist of a continuous distribution of energy over all space, the energy density tending to zero at infinity.

To achieve this aim, we introduce into the theory of general relativity the postulate that the gravitational, electric and nuclear fields are special cases of a more general field. An expression is obtained for the gravitational potential which differs from the usual expression of the potential accepted in general relativity, and which gives an energy density for the particle at every point of space, the integral of which over all space is equal to the mass of the particle, the greatest part of the mass being concentrated near the center of the spherical pattern constituting the particle.
When inserted in Dirac's wave equation, this potential gives the values of the masses of baryons. When inserted in the Klein-Gordon equation, this potential gives the values of the masses of mesons.
The particle is thus seen to consist of the energy of its field. No infinities are encountered in the integration's. The same result is obtained for a charged particle.