The Meson Field and Equations of Motion of Point Particles

The equation of motion of a point particle possessing a charge and interacting with a meson field (both vector and scalar) is derived from a generalization of the scheme of Infeld and Wallace for determining the equation of a point electron in an electromagnetic field. The retarded and advanced meson fields of the point particle and the nature of the simultaneous expressions for the symmetric, ½(ret+adv), and radiation, ½(ret-adv), potentials and field intensities are investigated. The simultaneous radiation field is found to be always finite for $r\to 0$, whereas the corresponding symmetric field allows expansion in powers of $r$ with -2 as the lowest, $r$ being the radius of the 3-dimensional sphere surrounding the singularity which represents the point particle. It is shown that the removal of the singularities from the symmetric field leads to the equation of motion given by Bhabha for the vector meson field in the case of the retarded field; the symmetric field, on the other hand, leads to the equation of motion in which the radiation damping is absent. The corresponding equation of motion of a point particle in a scalar meson field is also given.