  In this paper we first show that on projective manifolds (M, {\omega}), there
are holomorphic determinant bundles (in the sense of Knusden-Mumford used by
Bismut, Gillet, Soule) which play the role of the geometric quantum bundle,
namely one for each input data of a Hermitian holomorphic line bundle L of
non-trivial Chern class on a compact Kahler manifold Z (with Todd genus
non-zero) and a choice of a geometric quantization of (M, {\omega}). Next we
further study the generalization of the vortex equations on Kahler 4-manifold
which has been studied earlier by Bradlow. We show that when the Kahler
4-manifold avoids some obstructions then the regular part of the moduli space
is a Kahler manifold and admit a pull back of a Quillen determinant bundle as
the quantum line bundle, i.e. the curvature is proportional to the Kahler form.
Thus they can be quantized geometrically. In fact we show that the moduli space
of the usual vortex equations on a projective Kahler 4-manifold is projective
when the moduli space is smooth. Since in Kahler 4-manifold the vortex moduli
and the Seiberg Witten moduli coincide our effort gives a quantization of
Seiberg Witten moduli by determinant bundles
