  In this paper the Martin-Siggia-Rose (MSR) functional integral representation
is used for the study of the Langevin dynamics of a polymer melt in terms of
collective variables: mass density and response field density. The resulting
generating functional (GF) takes into account fluctuations around the random
phase approximation (RPA) up to an arbitrary order. The set of equations for
the correlation and response functions is derived. It is generally 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 considered and it is shown that
this results in a smearing out of the ideal glass 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 explicit expression for the memory
kernel was obtained and discussed in a qualitative link to the mode-coupling
equation.
