Dynamics of polymeric manifolds in melts: the Hartree approximation

The Martin-Siggia-Rose functional technique and the selfconsistent Hartree approximation is applied to the dynamics of a D-dimensional manifold in a m elt of similar manifolds. The generalized Rouse equation is derived and its static and dynamic properties are studied. The static upper critical dimen sion, d(uc) = 2D/(2 - D), discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, (d) over tilde(uc) = 2d(uc), discriminates between Rouse- and renormalized-Rouse behavior. Th e Rouse modes correlation function in a stretched exponential form and the dynamical exponents are calculated explicitly. The special case of linear c hains D = 1 shows agreement with Monte-Carlo simulations.