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Dynamical Supersymmetric Dirac Hamiltonians

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Abstract

Most recently a relativistic quantum mechanical approach to nuclear physics has proven promising.1 However we know from the interacting boson model of nuclei2 and the fermion dynamical symmetry model of nuclei3–5 that nuclear spectra exhibit dynamical symmetries.* Perhaps these symmetries have their basis in a realtivistic theory, particularly since the spinorbit potential is a relativistic effect. For this reason I would like to explore in this Symposium certain Dirac Hamiltonians, although I don’t pretend to come anywhere near the above-stated goal in this talk. The Dirac Hamiltonian I would like to consider is that of a neutral fermion interacting with a tensor field, say for example the electromagnetic field tensor. In this paper I shall use the language of QED since it is our best known realtivistic quantum theory. However, the Hamiltonians can have a more general applicability for example to QHD1 or QCD6.

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References

  1. B. D. Serot and J. D. Walecka, The Relativistic Nuclear Many-Body Problem, Adv. in Nuclear Physics, 16:1 (1986).

    Google Scholar 

  2. A. Arima and F. Iachello, The Interacting Boson Model, Adv. in Nuclear Physics, 13:139 (1984).

    Article  CAS  Google Scholar 

  3. J. N. Ginocchio, A Schematic Model for Monopole and Quadrupole Pairing in Nuclei, Ann. Phys., 126: 234 (1980).

    Article  CAS  Google Scholar 

  4. C. L. Wu, D. H. Feng, X. G. Chen, J. Q. Chen, and M. W. Guidry, A Fermion Dynamical Symmetry Model and the Nuclear Shell Model, Phys. Lett. 168B: 313 (1986).

    Article  Google Scholar 

  5. M. W. Guidry, C. L. Wu, D. H. Feng, and J. N. Ginocchio, A Fermion Dynamical Symmetry Model for High Spin Physics, Los Alamos preprint LA-UR-86–407, to be published in Phys. Lett. (1986).

    Google Scholar 

  6. I. J. R. Aitchison, An Informal Introduction to Gauge Field Theories, Cambridge University Press, New York (1982).

    Book  Google Scholar 

  7. E. Witten, Constraints on Supersymmetry Breaking, Nucl.Phvs. B202: 253 (1982).

    Article  Google Scholar 

  8. F. Cooper and B. Freedman, Aspects of Supersymmetric Quantum Mechanics, Ann. Phys., 146: 262 (1983).

    Article  CAS  Google Scholar 

  9. H. Ui, Supersymmetric Quantum Mechanics in Three-Dimensional Space. I, Prog. Theor. Phys. 72: 813 (1984).

    Article  CAS  Google Scholar 

  10. N. V. V. J. Swamy, Exact Solution of the Dirac Equation with an Equivalent Oscillator Potential, Phys. Rev. 180: 1225 (1969).

    Article  Google Scholar 

  11. Y. M. Cho, A Potential Approach to Spinor Quarks, Il Nuovo Cimento 23A: 550 (1974).

    Article  Google Scholar 

  12. A. B. Balantekin, Accidental Degeneracies and Supersymmetric Quantum Mechanics, Ann. Phys. 164: 277 (1986).

    Google Scholar 

  13. V. A. Kostelecky, M. M. Nieto, and D. R. Truax, Supersymmetry and the Relationship Between Coulomb and Oscillator Problems in Arbitrary Dimensions, to be published in Phys. Rev. D.

    Google Scholar 

  14. H. Ui and G. Takeda, Does Accidential Degeneracy Imply a Symmetry Group?, Prog. Theor. Phys. 72: 266 (1984).

    Article  CAS  Google Scholar 

  15. M. Moshinsky and C. Quesne, Does Accidental Degeneracy Imply a Symmetric Group?, Ann. Phys. 148: 462 (1983).

    Article  Google Scholar 

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Ginocchio, J.N. (1986). Dynamical Supersymmetric Dirac Hamiltonians. In: Gruber, B., Lenczewski, R. (eds) Symmetries in Science II. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1472-2_14

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  • DOI: https://doi.org/10.1007/978-1-4757-1472-2_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-1474-6

  • Online ISBN: 978-1-4757-1472-2

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