Skip to main content
Log in

Bundle of quantizations of a symplectic torus

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

For a given symplectic torus (M=V/Λ,ω) we construct a bundle whose base is the space of complex structures onV, and whose fibres are the corresponding quantizations ofM. We prove that there is no trivializations of this bundle which allow us to define a continuous identification of the quantizations.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bott, R. and Tu, L.:Differential Forms in Algebraic Topology, Springer-Verlag, New York, 1986.

    Google Scholar 

  2. Cartan, H.: Quotients of complex analytic spaces,Contributions to Function Theory, Tata Institute of Fundamental Research, Bombay, 1960, pp. 1–15.

    Google Scholar 

  3. Griffiths, P. and Harris, J.:Principles of Algebraic Geometry, Wiley, New York, 1978.

    Google Scholar 

  4. Guillemin, V. and Sternberg, S.,Symplectic Techniques in Physics, Cambridge Univ. Press, Cambridge, 1984.

    Google Scholar 

  5. Hitchin, N.: Flat connections and geometric quantization,Comm. Math. Phys. 131 (1990), 347–380.

    Google Scholar 

  6. Igusa, J.:Theta Functions, Springer-Verlag, Berlin, Heidelberg, 1972.

    Google Scholar 

  7. Kempf, G.:Complex Abelian Varieties and Theta Functions, Springer-Verlag, Berlin, Heidelberg, 1991.

    Google Scholar 

  8. Kobayashi, S.:Differential Geometry of Complex Vector Bundles, Iwana Shoten Publishers, Princeton Univ. Press, Princeton, N.J., 1987.

    Google Scholar 

  9. Lange, H. and Birkenhake, C.:Complex Abelian Varieties, Springer-Verlag, Berlin, Heidelberg, 1992.

    Google Scholar 

  10. Steenrod, N.:The Topology of Fibre Bundles, Princeton Univ. Press, Princeton, N. J., 1951.

    Google Scholar 

  11. Viña, A.: Bundle of Kähler quantizations, to be published.

  12. Weil, A.:Variétés kählériennes, Hermann, Paris, 1971.

    Google Scholar 

  13. Wells, R. O.:Differential Analysis on Complex Manifolds, Springer-Verlag, New York, 1980.

    Google Scholar 

  14. Woodhouse, N. M. J.:geometric Quantization, Clarendon Press, Oxford, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Viña, A. Bundle of quantizations of a symplectic torus. Lett Math Phys 36, 231–245 (1996). https://doi.org/10.1007/BF00943277

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00943277

Mathematics Subject Classifications (1991)

Key words

Navigation