The Supersymmetry and Eigen Energy Spectrum of a Charged Dirac Particle in a Uniform Constant Magnetic Field |
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Authors: | JIA Wen-Zhi WANG Shun-Jin |
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Institution: | Center of Theoretical Physics, Department of Physics, Sichuan University, Chengdu 610064, China2 Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, China |
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Abstract: | Based on the opinion that the γ-matrices in Dirac equation have structure and are decomposable, we decompose the γ-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. |
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