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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 123
On the Real Polarization of Chern-Simons Theory K. Mohnke
A construction of the Hilbert space of a $2+1$--dimensional topological quantum field theory due to Lisa Jeffrey and Jonathan Weitsman is studied in detail. We complete the argument for isotropy of the leaves of a certain foliation on the moduli space of flat ${f SU(2)}$--connections. This defines a real polarization of the prequantum system. Then the Hilbert space is defined to be generated by the set of `Bohr--Sommerfeld--leaves`, i.e. of those leaves admitting a parallel section in the prequantum line bundle. The characterization of these leaves is done alternatively using arguments familiar in general constructions of TQFT.
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