Fluctuation-dissipation-relation-preserving field theory of the glass transition in terms of fluctuating hydrodynamics

A field theoretical method for fluctuating hydrodynamics with preserved fluctuation-dissipation relations is reformulated. By assuming that the correlations including momentum are irrelevant in the long time region, we demonstrate that the equation obtained from the first-order perturbation is reduced to that for standard mode-coupling theory.

Figure 1

A diagram of the self-energy ${\Sigma }_{\widehat{\rho }\widehat{\varphi }}$ produced by vertex $V_{\widehat{\rho }\rho {\nu }_{\alpha }}$. From Eq. (40), the first-loop order self-energy on the left-hand side of the figure can be treated as a second-loop order one as shown on the right-hand side of the figure.