  We discuss the quantization of a class of relativistic fluid models defined
in terms of one real and two complex conjugate potentials with values on a
K\"{a}hler manifold, and parametrized by the K\"{a}hler potential
$K(z,\bar{z})$ and a real number $\lambda$. In the hamiltonian formulation, the
canonical conjugate momenta of the potentials are subjected to second class
constraints which allow us to apply the symplectic projector method in order to
find the physical degrees of freedom and the physical hamiltonian. We construct
the quantum theory for that class of models by employing the canonical
quantization methods. We also show that a semiclassical theory in which the
K\"{a}hler and the complex potential are not quantized has a highly degenerate
vacuum. Also, we define and compute the quantum topological number (quantum
linking number) operator which has non-vanishing contributions from the
K\"{a}hler and complex potentials only. Finally, we show that the vacuum and
the states formed by tensoring the number operators eigenstates have zero
linking number and show that linear combinations of the tensored number
operators eigenstates which have the form of entangled states have non-zero
linking number.
