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We investigated the relativistic dynamics of oppositely charged two fermionsinteracting with an external uniform magnetic field. We chose the interactionof each fermion with the external magnetic field in the symmetric gauge, andobtained a precise solution of the corresponding fully-covariant two-body Diracequation that derived from Quantum Electrodynamics via Action principle. Thedynamic symmetry of the system we deal with allowed us to determine therelativistic Landau levels of such a spinless composite system, without usingany group theoretical method. As a result, we determined the eigenfunctions andeigenvalues of the corresponding two-body Dirac Hamiltonian

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