Multipole Singularities of Classical Scalar and Pseudoscalar Meson Fields

Abstract

The general form of the equations of motion of a particle possessing multipole singularities of a neutral scalar or pseudoscalar meson field has been found by Harish-Chandra on the basis of Dirac's method. In this paper the general form of the multipole moment compatible with these equations is established under the assumption that the spin and the ${2}^{n}$-pole moments of the particle are of constant magnitude and have only spatial components in the system in which the particle is at rest. Then the general form of the equations of motion and of the multipole moment compatible with them is established for point particles interacting with a charge-symmetric scalar or pseudoscalar meson field. It is found that ${2}^{n}$-pole moments of different types are possible for arbitrary $n$, and that a particle can carry an arbitrary combination of such moments.