Skip to main content

Formal quantization of quadratic momentum observables

  • E. Symplectic Geometry and Quantization
  • Conference paper
  • First Online:
The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function

Part of the book series: Lecture Notes in Physics ((LNP,volume 278))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. M. J. Gotay, Int. J. Theor. Phys., 19, 139 (1980).

    Article  Google Scholar 

  3. R. Abraham and J. E. Marsden, Foundations of Mechanics (Benjamin-Cummings, Reading, PA, 1978).

    MATH  Google Scholar 

  4. H.J. Groenewold, Physica, 12, 405 (1946).

    Article  ADS  MathSciNet  Google Scholar 

  5. A. Joseph, Commun. Math. Phys., 17, 210 (1970).

    Article  ADS  Google Scholar 

  6. P. Chernoff, Had. J., 4, 879 (1981).

    Google Scholar 

  7. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Ann. Phys., 111, 111 (1978).

    Article  ADS  Google Scholar 

  8. P. B. Guest, Rep. Math. Phys., 6, 99 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  9. W. Arveson, Commun. Math. Phys., 89, 77 (1983).

    Article  ADS  Google Scholar 

  10. J. Underhill, J. Math. Phys., 19, 1932 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  11. F. J. Bloore, in Géométrie Symplectique'et Physique Mathématique, Coll. Int. C.N.R.S. 237, 299 (1978).

    Google Scholar 

  12. B. Kostant, in Géométrie Symplectique et Physique Mathématique, Coll. Int. C.N.R.S. 237, 187 (1978).

    Google Scholar 

  13. J. Sniatycki, Geometric Quantization and Quantum Mechanics, Springer Appl. Math. Ser. 30 (Springer, Berlin, 1980).

    Google Scholar 

  14. N. M. J. Woodhouse, Geometric Quantization (Clarendon, Oxford, 1980).

    MATH  Google Scholar 

  15. I. Vaisman, J. Austral. Math. Soc., 23, 394 (1982).

    Article  Google Scholar 

  16. R. Hermann, Lie Algebras and Quantum Mechanics, (Benjamin, New York, 1970).

    MATH  Google Scholar 

  17. R. Geroch, Geometrical Quantum Mechanics, mimeographed lecture notes (Univ. of Chicago, 1975).

    Google Scholar 

  18. R. J. Blattner, in LNM 570, 11 (1977).

    Google Scholar 

  19. J. von Neumann, Mathematical Foundations of Quantum Mechanics, (Princeton, 1955).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Y. S. Kim W. W. Zachary

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Gotay, M.J. (1987). Formal quantization of quadratic momentum observables. In: Kim, Y.S., Zachary, W.W. (eds) The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function. Lecture Notes in Physics, vol 278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17894-5_384

Download citation

  • DOI: https://doi.org/10.1007/3-540-17894-5_384

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17894-1

  • Online ISBN: 978-3-540-47901-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics