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A field theoretical method for the fluctuating hydrodynamics with preservingfluctuation-dissipation relations (FDR) is reformulated. It is shown that thelong time behavior within the first-loop order perturbation under theassumption that the correlations include the momentum decay fast enough, isequivalent to that for the standard mode-coupling theory.

A FDR-preserving field theory of glass transition in terms of the fluctuating hydrodynamics