Chinese Physics C > 2006, Vol. 30 > Issue(6): 530-536

The Supersymmetry and Eigen Energy Spectrum of a Charged Dirac Particle in a Uniform Constant Magnetic Field

JIA Wen-Zhi,
WANG Shun-Jin^,

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.

References

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JIA Wen-Zhi and WANG Shun-Jin. The Supersymmetry and Eigen Energy Spectrum of a Charged Dirac Particle in a Uniform Constant Magnetic Field[J]. Chinese Physics C, 2006, 30(6): 530-536.

JIA Wen-Zhi and WANG Shun-Jin. The Supersymmetry and Eigen Energy Spectrum of a Charged Dirac Particle in a Uniform Constant Magnetic Field[J]. Chinese Physics C, 2006, 30(6): 530-536. shu

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Received: 2005-12-04
Revised: 2005-12-13

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沈阳化工大学材料科学与工程学院沈阳 110142

The Supersymmetry and Eigen Energy Spectrum of a Charged Dirac Particle in a Uniform Constant Magnetic Field

JIA Wen-Zhi
WANG Shun-Jin^,

Corresponding author:WANG Shun-Jin,

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

Received Date:2005-12-04
Accepted Date:2005-12-13
Available Online:2006-06-05

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.