Advertisement

On geometric quantization

  • R. J. Blattner
Part II Quantization Procedures
Part of the Lecture Notes in Mathematics book series (LNM, volume 1037)

Keywords

Hilbert Space Vector Field Line Bundle Poisson Bracket Symplectic Manifold 
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]
    Avez, A., Lichnerowicz, A., and Diaz Miranda, A., "Sur l'algèbra des automorphismes infinitésimaux d'une variété symplectique", J. Differential Geometry 9 (1974), 1–40MathSciNetzbMATHGoogle Scholar
  2. [2]
    Blattner, R.J., "Quantization and representation theory" in Proc. Sympos. Pure Math., vol. 26, Amer. Math. Soc., Providence, 1973Google Scholar
  3. [3]
    Blattner, R.J., "The metalinear geometry of non-real polarizations" in Lec. Notes in Mathematics, vol. 570, Springer-Verlag, Berlin, 1977Google Scholar
  4. [4]
    Blattner, R.J., and Rawnsley, J.H., "Quantization of the action of U(k,1) on R2(k+1), J. Functional Analysis 50 (1983), 188–214MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Dirac, P.A.M., "The Principles of Quantum Mechanics", 3rd ed., Clarendon Press, Oxford, 1947zbMATHGoogle Scholar
  6. [6]
    Guillemin, V.W. and Sternberg, S., "Geometric Asymptotics", Amer. Math. Soc., Providence, 1977zbMATHGoogle Scholar
  7. [7]
    Kostant, B., "Quantization and unitary representations" in Lecture Notes in Mathematics, vol. 170, Springer-Verlag, Berlin, 1970Google Scholar
  8. [8]
    Kostant, B., "Symplectic spinors" in Symposia Math., vol. XIV, Academic Press, London, 1974Google Scholar
  9. [9]
    Palais, R.S., "A global formulation of the Lie theory of transformation groups", Mem. Amer. Math. Soc. 22 (1957)Google Scholar
  10. [10]
    Rawnsley, J.H., "On the cohomology groups of a polarisation and diagonal quantisation", Trans. Amer. Math. Soc. 230 (1977), 235–255MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Rawnsley, J.H., "On the pairing of polarisations", Comm. Math. Phys. 58 (1978), 1–8MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    Rawnsley, J.H., Schmid, W., and Wolf, J.A., "Singular unitary representations and indefinite harmonic theory", J. Functional Analysis 51 (1983), 1–114MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    Segal, I.E., "Quantization of nonlinear systems", J. Math. Phys. 1 (1960), 468–488zbMATHCrossRefGoogle Scholar
  14. [14]
    Śniatycki, J., "Geometric Quantization and Quantum Mechanics", Applied Mathematical Sciences, vol. 30, Springer-Verlag, Berlin, 1980Google Scholar
  15. [15]
    Souriau, J.-M., "Structure des systèmes dynamiques", Dunod, Paris, 1970Google Scholar
  16. [16]
    Urwin, R.W., "The prequantization representations of the Poisson Lie algebra", Advances in Math., to appearGoogle Scholar
  17. [17]
    van Hove, L., "Sur certains représentations unitaires d'un groupe infini de transformations", Acad. roy. Belg. Classe sci. Mém. Collection in 80 26 (1951), no.6, 1–102Google Scholar
  18. [18]
    Wells, R.O., Jr., "Differential Analysis on Complex Manifolds", Prentice-Hall, Englewood Cliffs, 1973zbMATHGoogle Scholar
  19. [19]
    Weinstein, A., "Symplectic manifolds and their Lagrangian submanifolds", Advances in Math. 6 (1971), 329–346MathSciNetzbMATHCrossRefGoogle Scholar
  20. [20]
    Woodhouse, N., "Geometric Quantization", Clarendon Press, Oxford, 1980.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • R. J. Blattner
    • 1
  1. 1.Department of MathematicsUCLALos Angeles

Personalised recommendations