  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 for 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 {\em dynamic} critical phenomenon. The transition to the entangled state is
also shown to be a critical point. For larger concentrations, when the role of
fluctuations is reduced, a mean field approximation is justifiably employed to
show the existence of tube-like structures reminiscent of Edwards' model.
