Abstract:
In this talk we explain what geometric quantization is and describe the geometric quantization of the moduli space of flat connections using Witten -Quillen determinant line bundle construction which appears in (2+1)-dimensional Chern-Simons topological field theory. Then we modify this construction to construct determinant line bundles on the moduli space of Hitchin's self-dual Yang-Mills equations on a Riemann surface and also for the moduli space of vortex equations. This enables us to geometrically quantize these two systems. In fact the hyperKahler structure in the Hitchin system can be quantized this way. For the vortex moduli space we find a whole family of determinant line bundles corresponding to a family of symplectic forms.
