Physics of polymer melts

We have mapped the physics of polymer melts onto a time-dependent Landau-Ginzburg \psi\(4) field theory using techniques of functional integration. Time in the theory is simply a label fur the location of a given monomer along the extent of a flexible chain. With this model, one can show that the limit of infinitesimal concentration of a polymer melt corresponds to a dynamic critical phenomenon. The transition to the entangled stare is also shown to be a critical point. For larger concentrations, when the role of fluctuations is reduced, a mean-held approximation is justifiably employed to show the existence of tubelike structures reminiscent of Edwards' model.