Advertisement

Formal quantization of quadratic momentum observables

  • Mank J. Gotay
E. Symplectic Geometry and Quantization
Part of the Lecture Notes in Physics book series (LNP, volume 278)

Keywords

Semiclassical Limit Vertical Polarization Classical Observable Hamiltonian Vector Field Momentum Observable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Van Hove, Acad. Roy. Belg. Bull. C1. Sci., (5), 37, 610 (1951); Mem. Acad. Roy. Belg., (6), 26, 1 (1951).Google Scholar
  2. 2.
    M. J. Gotay, Int. J. Theor. Phys., 19, 139 (1980).CrossRefGoogle Scholar
  3. 3.
    R. Abraham and J. E. Marsden, Foundations of Mechanics (Benjamin-Cummings, Reading, PA, 1978).MATHGoogle Scholar
  4. 4.
    H.J. Groenewold, Physica, 12, 405 (1946).ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    A. Joseph, Commun. Math. Phys., 17, 210 (1970).ADSCrossRefGoogle Scholar
  6. 6.
    P. Chernoff, Had. J., 4, 879 (1981).Google Scholar
  7. 7.
    F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Ann. Phys., 111, 111 (1978).ADSCrossRefGoogle Scholar
  8. 8.
    P. B. Guest, Rep. Math. Phys., 6, 99 (1974).ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    W. Arveson, Commun. Math. Phys., 89, 77 (1983).ADSCrossRefGoogle Scholar
  10. 10.
    J. Underhill, J. Math. Phys., 19, 1932 (1978).ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    F. J. Bloore, in Géométrie Symplectique'et Physique Mathématique, Coll. Int. C.N.R.S. 237, 299 (1978).Google Scholar
  12. 12.
    B. Kostant, in Géométrie Symplectique et Physique Mathématique, Coll. Int. C.N.R.S. 237, 187 (1978).Google Scholar
  13. 13.
    J. Sniatycki, Geometric Quantization and Quantum Mechanics, Springer Appl. Math. Ser. 30 (Springer, Berlin, 1980).Google Scholar
  14. 14.
    N. M. J. Woodhouse, Geometric Quantization (Clarendon, Oxford, 1980).MATHGoogle Scholar
  15. 15.
    I. Vaisman, J. Austral. Math. Soc., 23, 394 (1982).CrossRefGoogle Scholar
  16. 16.
    R. Hermann, Lie Algebras and Quantum Mechanics, (Benjamin, New York, 1970).MATHGoogle Scholar
  17. 17.
    R. Geroch, Geometrical Quantum Mechanics, mimeographed lecture notes (Univ. of Chicago, 1975).Google Scholar
  18. 18.
    R. J. Blattner, in LNM 570, 11 (1977).Google Scholar
  19. 19.
    J. von Neumann, Mathematical Foundations of Quantum Mechanics, (Princeton, 1955).Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Mank J. Gotay
    • 1
  1. 1.Mathematics DepartmentUnited States Naval AcademyAnnapolis

Personalised recommendations