Incorporation of anomalous magnetic moments in the two-body relativistic wave equations of constraint theory

TL;DR

This paper develops a method to incorporate anomalous magnetic moments into two-body relativistic wave equations, revealing how these moments modify the potential and affect the equations' structure and solutions.

Contribution

It introduces a local form of anomalous magnetic moments into two-body relativistic wave equations using a Dirac-matrix substitution, extending the theory's applicability.

Findings

Derived the potential structure with anomalous magnetic moments

Reduced wave equations to a single eigenvalue form in specific sectors

Analyzed the nonrelativistic limit of the equations

Abstract

Using a Dirac-matrix substitution rule, applied to the electric charge, the anomalous magnetic moments of fermions are incorporated in local form in the two-body relativistic wave equations of constraint theory. The structure of the resulting potential is entirely determined, up to magnetic type form factors, from that of the initial potential descibing the mutual interaction in the absence of anomalous magnetic moments. The wave equations are reduced to a single eigenvalue equation in the sectors of pseudoscalar and scalar states ($j=0$). The requirement of a smooth introduction of the anomalous magnetic moments imposes restrictions on the behavior of the form factors near the origin, in $x$-space. The nonrelativistic limit of the eigenvalue equation is also studied.