Two-Body Mass-Shell Constraints in a Constant Magnetic Field (Neutral Case)

TL;DR

This paper develops a covariant framework to analyze a two-particle scalar system in a constant magnetic field, deriving a reduced eigenvalue problem that respects relativistic symmetry and accounts for collective motion.

Contribution

It introduces a novel covariant method to handle two-body mass-shell constraints in a magnetic field, including collective variables and motional effects.

Findings

Derived a 3D reduced eigenvalue equation for the system.

Ensured relativistic symmetry is maintained in the formulation.

Accounted for collective motion effects in the relativistic framework.

Abstract

A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a suitable representation. The relativistic symmetry associated with the magnetic field is carefully respected. Considering eigenstates of the pseudo momentum four-vector, we separate out collective variables and obtain a 3- dimensional reduced equation, posing a nonconventional eigenvalue problem. The velocity of the system as a whole generates "motional" terms in the formulas these terms are taken into account within a manifestly covariant framework.