The relativistic dynamics of oppositely charged two fermions interacting with external uniform magnetic field

TL;DR

This paper provides an exact solution to the relativistic two-body Dirac equation for oppositely charged fermions in a uniform magnetic field, revealing their Landau levels and eigenstates without group theory.

Contribution

It introduces a precise, covariant approach to solve the two-body Dirac equation in an external magnetic field, deriving eigenfunctions and eigenvalues analytically.

Findings

Determined the relativistic Landau levels for the system.

Obtained explicit eigenfunctions and eigenvalues.

Demonstrated a symmetry-based method without group theory.

Abstract

We investigated the relativistic dynamics of oppositely charged two fermions interacting with an external uniform magnetic field. We chose the interaction of each fermion with the external magnetic field in the symmetric gauge, and obtained a precise solution of the corresponding fully-covariant two-body Dirac equation that derived from Quantum Electrodynamics via Action principle. The dynamic symmetry of the system we deal with allowed us to determine the relativistic Landau levels of such a spinless composite system, without using any group theoretical method. As a result, we determined the eigenfunctions and eigenvalues of the corresponding two-body Dirac Hamiltonian