On the theory of a scalar particle with electromagnetic polarizability in Coulomb and Dirac monopole fields

TL;DR

This paper develops a matrix and tetrad-based theoretical framework for a scalar particle with charge and polarizability in Coulomb and monopole fields, deriving radial equations with an r^{-4} potential term highlighting monopole effects.

Contribution

It introduces a novel 15-component wave equation approach for scalar particles with electromagnetic polarizability in external fields, including Coulomb and magnetic monopole fields.

Findings

Radial equations reduce to a generalized Klein-Fock form with r^{-4} term.

Monopole influence is more significant due to the r^{-4} potential.

The approach allows separation of variables and detailed analysis of particle-field interactions.

Abstract

15-component matrix and tetrad-based description of a a scalar particle with two electromagnetic characteristics -- charge e and polarizability \sigma, is elaborated in presence of external Coulomb field. With the use of Wigner's D-functions, in the basis of diagonal spherical tetrad, the separation of variables in the generalized wave equation is done, and a system of 15 radial equations is given. It is shown that the radial system is reduced to a generalized Klein-Fock radial equation with an additional term of the form r^{-4}. In the framework of the analogous approach a scalar particle with charge e and polarizability \sigma is investigated in presence of the field of a magnetic charge g. The separation of variables is done. Again all the radial system is reduced to a single differential equation of second order with an additional term of the form r^{-4} . This means that because of the known peculiar properties of the potential r^{-4} (an absorbing center), the monopole influence on the scalar particle with \sigma -characteristics is much more noticeable in the radial equation than in the case of usual particle.