Geometric prequantization of the moduli space of the vortex equations on a Riemann surface

摘要

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact, Kahler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, Kahler) structures Omega(Psi 0) on the moduli space, parametrized by Psi(0), a section of a line bundle on the Riemann surface. Next, we show that corresponding to these, there is a family of prequantum line bundles P-Psi 0 on the moduli space whose curvature is proportional to the symplectic forms Omega(Psi 0). (c) 2006 American Institute of Physics.