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Remarks on the geometric quantization of the Kepler problem

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Abstract

The geometric quantization of the (three-dimensional) Kepler problem is readily obtained from the one of the harmonic oscillator using a Segre map. The physical meaning of the latter is discussed.

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References

  1. SimmsD. J., Geometric Quantization of the Energy Levels in the Kepler Problem, Symposia Mathematica, vol. XIV, INDAM, Rome, 1973, Academic Press, New York, 1974.

    Google Scholar 

  2. StiefelE. L. and ScheifeleG., Linear and Regular Celestial Mechanics, Springer, Berlin, 1971.

    Google Scholar 

  3. KummerM., On the regularization of the Kepler problem, Commun. Math. Phys. 84, 133–152 (1982).

    Google Scholar 

  4. LandauL. and LifshitzE., Quantum Mechanics, Pergamon, London, 1960.

    Google Scholar 

  5. GarbaczewskyP., Stochastic mechanics and the Kepler problem, Phys. Rev. D 33, 2916–2921 (1986).

    Google Scholar 

  6. GriffithsP. and HarrisJ., Principles of Algebraic Geometry, Wiley, N.Y., 1978.

    Google Scholar 

  7. RawnsleyJ. H., Coherent states and Kähler manifolds, Quart. J. Math. Oxford 28, 403–415 (1977).

    Google Scholar 

  8. HurtN., Geometric Quantization in Action, D. Reidel, Dordrecht, 1983.

    Google Scholar 

  9. SouriauJ. M., Sur la variété de Kepler, Symposia Mathematica, vol. XIV, INDAM Rome, 1973, Academic Press, New York, 1974.

    Google Scholar 

  10. CordaniR., Conformal regularization of the Kepler problem, Commun. Math. Phys. 103, 403–413 (1986).

    Google Scholar 

  11. CordaniB. and ReinaC., Spinor regularization of the n-dimensional Kepler problem, Lett. Math. Phys. 13, 79–82 (1987).

    Google Scholar 

  12. OnofriE., Dynamical quantization of the Kepler manifold, J. Math. Phys. 17, 401–408 (1976).

    Google Scholar 

  13. SimmsD. J. and WoodhouseN., Lectures on Geometric Quantization, LNP 53, Springer, Berlin, 1976.

    Google Scholar 

  14. PerelomovA. M., Generalized Coherent States and Their Applications, Springer, Berlin, 1986.

    Google Scholar 

  15. HodgeW. V. D., Some enumerative results in theory of forms, Proc. Camb. Phil. Soc. 39, 22–30 (1943).

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica, I Universita' di Roma, 00185, Rome, Italy

    Giuseppe Gaeta

  2. Dipartimento di Matematica, II Universita' di Roma, 00173, Rome, Italy

    Mauro Spera

Authors
  1. Giuseppe Gaeta
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  2. Mauro Spera
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Gaeta, G., Spera, M. Remarks on the geometric quantization of the Kepler problem. Lett Math Phys 16, 189–197 (1988). https://doi.org/10.1007/BF00398955

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  • DOI: https://doi.org/10.1007/BF00398955

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