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.

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带相反电荷的两个费米子与外部均匀磁场相互作用的相对论动力学

我们研究了带相反电荷的两个费米子与外部均匀磁场相互作用的相对论动力学，而没有考虑费米子之间的任何电荷-电荷相互作用。我们在对称规范中选择了每个费米子与外部磁场的相互作用，并通过作用原理从量子电动力学中获得了相应的全协变二体狄拉克方程的精确解。我们处理的系统的动态对称性使我们能够确定这种无自旋复合系统的相对论朗道能级，而无需使用任何群论方法。结果，我们确定了相应的二体狄拉克哈密顿量的特征函数和特征值。