Langevin dynamics of the glass forming polymer melt: Fluctuations around the random phase approximation

In this paper the Martin-Siggia-Rose (MSR) functional integral representati on is used for the study of the Langevin dynamics of a polymer melt in term s of collective variables: mass density and response field density. The res ulting generating functional (GF) takes into account fluctuations around th e random pha,se approximation (RPA) up to an arbitrary order. The set of eq uations for the correlation and response functions is derived. It is genera lly shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively consid ered and it is shown that this: results in a smearing out of the ideal glas s transition. The memory kernel is specified for the ideal glass transition as a sum of all "water-melon" diagrams. For the Gaussian chain model the e xplicit expression for the memory kernel was obtained and discussed in a qu alitative link to the mode-coupling equation.