Fluctuating nonlinear hydrodynamics and the liquid-glass transition

We study the fluctuating nonlinear hydrodynamics of compressible fluids. Development of the appropriate field-theoretical description for this problem requires treatment of nonlinearities which arise through the relationship g=, where g is the momentum density, is the mass density, and V is the velocity field. We show how this constraint can be naturally included in a field theory of the Martin-Siggia-Rose type. We analyze the structure of the resulting field theory using the available fluctuation-dissipation theorem. We also develop the perturbation-theory expansion in powers of the temperature and evaluate the contributions from the nonlinearities to one-loop order. We show that the theory is renormalizable in the hydrodynamic limit. This field-theoretical model is used to systematically investigate the origins and viability of the nonlinear density feedback mechanism first identified by Leutheusser as a source of the liquid-glass transition. While we find that the nonlinear couplings driving this mechanism are present, we also find contributions, arising from the nonlinear constraint relating g, , and V, which cut off the mechanism. The cutoff arises from a nonhydrodynamic correction not treated in previous work. While we find that there is no sharp transition, we do find evidence for a rounded version of the transition.