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Quantization via real polarization of the moduli space of flat connections and Chern-Simons gauge theory in genus one

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Abstract

We study the quantization of the moduli space of flat connections on a surface of genus one, using the real polarization of this space described in [10]. The quantum wave functions in this formalism are exponential functions supported along the integral fibres of the polarization. The space of wave functions obtained in this way is isomorphic to a space of theta functions. We use our construction to construct part of what may be a topological field theory in genus one, and to compute the associated invariants of some three manifolds. These computations agree with those of Witten [12], but the invariants are expressed as sums of quantities computed at a discrete set of connections with curvature concentrated on a link in the three manifold. A similar prescription is used to produce knot invariants.

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Authors and Affiliations

  1. Department of Mathematics, M.I.T., 02139, Cambridge, MA, USA

    Jonathan Weitsman

  2. Department of Physics, Harvard University, 02138, Cambridge, MA, USA

    Jonathan Weitsman

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  1. Jonathan Weitsman
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Additional information

Communicated by A. Jaffe

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

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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, 175–190 (1991). https://doi.org/10.1007/BF02099122

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  • DOI: https://doi.org/10.1007/BF02099122

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