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.
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
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.
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