  We study the role of the Jacobian arising from a constraint enforcing the
nonlinear relation: ${\bf g}=\rho{\bf V}$, where $\rho,\: {\bf g}$ and ${\bf
V}$ are the mass density, the momentum density and the local velocity field,
respectively, in the field theoretic formulation of the nonlinear fluctuating
hydrodynamics of simple fluids. By investigating the Jacobian directly and by
developing a field theoretic formulation without the constraint, we find that
no changes in dynamics result as compared to the previous formulation developed
by Das and Mazenko (DM). In particular, the cutoff mechanism discovered by DM
is shown to be a consequence of the $1/\rho$ nonlinearity in the problem not of
the constraint. The consequences of this result for the static properties of
the system is also discussed.
