Supersymmetry and eigen energy spectrum of a charged Dirac particle in a uniform constant magnetic field

Based on the opinion that the gamma-matrices in Dirac equation have structure and are decomposable, we decompose the gamma-matrices into the direct product of the operators in the spin space and the particle-antiparticle space. By using this method, we attain a complete set of commutative operators, a set of quantum numbers and the correspondingly eigen solutions of the Hamiltonian for a charged Dirac particle moving in a uniform constant magnetic field. In addition, the dynamic supersymmetry of the Hamiltonian is unveiled. Spin symmetry breaking and particle-antiparticle symmetry breaking are discussed, and the supersymmetric group operator of the degenerate spin subspace resulting from the spin residual supersymmetry is found.