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The Martin-Siggia-Rose (MSR) functional integral technique is applied to thedynamics of a D - dimensional manifold in a melt of similar manifolds. Theintegration over the collective variables of the melt can be simply implementedin the framework of the dynamical random phase approximation (RPA). Theresulting effective action functional of the test manifold is treated by makinguse of the selfconsistent Hartree approximation. As an outcome the generalizedRouse equation (GRE) of the test manifold is derived and its static and dynamicproperties are studied. It was found that the static upper critical dimension,$d_{\rm uc}=2D/(2-D)$, discriminates between Gaussian (or screened) andnon-Gaussian regimes, whereas its dynamical counterpart, ${\tilded}_{uc}=2d_{\rm uc}$, distinguishes between the simple Rouse and therenormalized Rouse behavior. We have argued that the Rouse mode correlationfunction has a stretched exponential form. The subdiffusional exponents forthis regime are calculated explicitly. The special case of linear chains, D=1,shows good agreement with MD- and MC-simulations.Comment: 35 pages,3 figures, accepted by J.Chem.Phy

The Hartree approximation in dynamics of polymeric manifolds in the melt