Skip to main content
SpringerLink
Log in

Real polarization of the moduli space of flat connections on a Riemann surface

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

Abstract

We prove that the moduli space of flatSU(2) connections on a Riemann surface has a real polarization, that is, a foliation by lagrangian subvarieties. This polarization may provide an alternative quantization of the Chern-Simons gauge theory in higher genus, in line with the results of [11] for genus one.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Atiyah, M.: Michaelmas notes, unpublished

  2. Atiyah, M., Bott, R.: The Yang-Mills equations over a Riemann surface. Phil. Trans. R. Soc.A308, 523 (1982)

    Google Scholar 

  3. Goldman, W.: Invariant Functions on Lie groups and Hamiltonian flows of surface group representations. Invent. Math.85, 263 (1986)

    Google Scholar 

  4. Guillemin, V., Sternberg, S.: Symplectic techniques in physics. Cambridge: Cambridge University Press 1980

    Google Scholar 

  5. Hitchin, N.: Stable Bundles and Integrable Systems. Duke Math. J.54, 91 (1987) — The self duality equations on a Riemann surface. Proc. Lond. Math. Soc.55, 59 (1987)

    Google Scholar 

  6. Jeffrey, L., Weitsman, J.: Bohr-Sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula. Institute for Advanced Study preprint IASSNS-HEP-91/82

  7. Jeffrey, L., Weitsman, J.: Half density quantization of the moduli space of flat connections and Witten's semiclassical manifold invariants. Institute for Advanced Study preprint IASSNS-HEP-91/94

  8. Ramadas, T., Singer, I. M., Weitsman, J.: Some comments on Chern-Simons gauge theory. Commun. Math. Phys.126, 409 (1989)

    Google Scholar 

  9. Segal, G.: The definition of conformal field theory, unpublished

  10. Sniatycki, J.: Geometric quantization and quantum mechanics. Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

  11. Weitsman, J.: Quantization via Real polarization of the moduli space of flat connections and Chern simons gauge theory in genus one. Commun. Math. Phys.137, 175 (1991)

    Google Scholar 

  12. Witten, E.: Quantum field theory and the Jones polynomial. Commun. Math. Phys.121, 359 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Jonathan Weitsman

Authors
  1. Jonathan Weitsman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. Jaffe

Supported by NSF Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weitsman, J. Real polarization of the moduli space of flat connections on a Riemann surface. Commun.Math. Phys. 145, 425–433 (1992). https://doi.org/10.1007/BF02099391

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02099391

Keywords

Search

Navigation