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

JIA Wen-Zhi; WANG Shun-Jin

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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. Rabi I I. Z. Phys., 1928, 9: 5072. Johnson M H, Lippmann B A. Phys. Rev., 1949, 76: 8283. Nieto M M, Taylor P L. Am. J. Phys., 1985, 53: 2344. MacDonald A H. Phys. Rev., 1983, B28: 22355. Chakrabarty S, Bandyopadhyay D, Pal S. Phys. Rev. Lett.,1997, 78: 28986. MAO Guang-Jun, Iwamoto A, LI Zhu-Xia. astro-ph/01092217. Hughes R J, Kostelrky V A, Nieto M M. Phys. Rev., D34:11008. Cooper F, Khare A, Sukhatme U P. Phys. Rep., 1995, 251:2679. WANG Shun-Jin, ZHOU Shan-Gui, Pauli H C. Review ofNuclear Physics, 2004, 21(1): 94-97(in Chinese)(王顺金，周善贵，Pauli H C.原f核物理评论，2004, 21(1):94-97)10. WANG Shun-Jin. Advanced Quantum Mechanics and Quantum Many Body Theory. Sichuan: Sichuan Univer-sity Press, 2005. 181?852005. 181—185)(in Chinese)(王顺金.高等量子论与量r多体理论.四川:四川大学出版社,2005. 181-185)11. WANG Shun-Jin, ZHOU Shan-Gui. hep-th/050125012. ZHANG Jian-Zu, LI Xin-Zhou, ZHANG Jiu-An et al. Phys.Rev., 1996, A54: 5418

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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.