Langevin dynamics of polymeric manifolds in melts

The Martin-Siggia-Rose generating functional (MSR-GF) technique is used for treating the polymeric D-dimensional-manifold melt dynamics. The one- (tes t-) manifold dynamics and the collective dynamics are considered separately . The test-manifold dynamics is obtained by integrating out the melt collec tive variables. This is done within the dynamic random-phase approximation (RPA). The resulting effective-action functional of the test manifold is tr eated by making use of the self-consistent Hartree approximation. As a cons equence, the generalized Rouse equation of the test manifold is derived, an d its static and dynamic properties are studied. By making use the MSR-GF t echnique, the fluctuations around the RPA of the collective variables-mass density and response-field density-are investigated. As a result, the equat ions for the correlation and response functions are derived. The memory ker nel can be specified for the ideal glass transition as a sum of all 'water- melon' diagrams.