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We study the role of the Jacobian arising from a constraint enforcing thenonlinear relation: ${\bf g}=\rho{\bf V}$, where $\rho,\: {\bf g}$ and ${\bfV}$ are the mass density, the momentum density and the local velocity field,respectively, in the field theoretic formulation of the nonlinear fluctuatinghydrodynamics of simple fluids. By investigating the Jacobian directly and bydeveloping a field theoretic formulation without the constraint, we find thatno changes in dynamics result as compared to the previous formulation developedby Das and Mazenko (DM). In particular, the cutoff mechanism discovered by DMis shown to be a consequence of the $1/\rho$ nonlinearity in the problem not ofthe constraint. The consequences of this result for the static properties ofthe system is also discussed.Comment: 17 pages (5 figs. upon request), ReVTEX 3.

Density nonlinearities and a field theory for the dynamics of simple fluids