  The self-duality equations on a Riemann surface arise as dimensional
reduction of self-dual Yang-Mills equations. Hitchin had showed that the moduli
space ${\mathcal M}$ of solutions of the self-duality equations on a compact
Riemann surface of genus $g >1$ has a hyperK\"{a}hler structure. In particular
${\mathcal M}$ is a symplectic manifold. In this paper we elaborate on one of
the symplectic structures, the details of which is missing in Hitchin's paper.
Next we apply Quillen's determinant line bundle construction to show that
${\mathcal M}$ admits a prequantum line bundle. The Quillen curvature is shown
to be proportional to the symplectic form mentioned above. We do it in two
ways, one of them is a bit unnatural (published in R.O.M.P.) and a second way
which is more natural.
