Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

Details Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

2006-05-08

arxiv.org/abs/math-ph/0605025v3

Journal of Mathematical Physics, vol. 47, issue 10, page 103501, 2006

Physics

Mathematical Physics

8 pages

Scientific paper

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures $\Omega_{\Psi_0}$ on the moduli space, parametrised 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 ${\mathcal P}_{\Psi_0} $on the moduli space whose curvature is proportional to the symplectic forms $\Omega_{\Psi_0}$.

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