Relativistic Dynamics of Oppositely Charged Two Fermions Interacting with External Uniform Magnetic Field

We investigated the relativistic dynamics of oppositely charged two fermions interacting with an external uniform magnetic field, without considering any charge-charge interaction between the fermions. 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.

Automated summary

This study investigated the relativistic dynamics of two oppositely charged fermions interacting with an external magnetic field, without considering charge-charge interaction. By choosing the symmetric gauge for the interaction with the magnetic field, a precise solution was obtained for the corresponding fully-covariant two-body Dirac equation. The dynamic symmetry of the system allowed for the determination of relativistic Landau levels without using group theoretical methods.