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A phase diagram for a 2D metal with variable carrier density has been studiedusing the modulus-phase representation for the order parameter in a fullymicroscopic treatment. This amounts to splitting the degrees of freedom intoneutral fermion and charged boson degrees of freedom. Although true long rangeorder is forbidden in two dimensions, long range order for the neutral fermionsis possible since this does not violate any continuous symmetry. The phasefluctuations associated with the charged degrees of freedom destroy long rangeorder in the full system as expected. The presence of the neutral orderparameter gives rise to new features in the superconducting condensateformation in low dimensional systems. The resulting phase diagram contains anew phase which lies above the superconducting (hereBerezinskii-Kosterlitz-Thouless) phase and below the normal (Fermi-liquid)phase. We identify this phase with the pseudogap phase observed in underdopedhigh-$T_{c}$ superconducting compounds above their critical temperature. Wealso find that the phase diagram persists even in the presence of weak3-dimensionalisation.Comment: 4 pages, LaTeX; invited paper presented at New^3SC-1, Baton Rouge,  USA, 1998. To be published in Int.J.Mod.Phys.

Pseudogap Phase Formation in the Crossover from Bose-Einstein Condensation to BCS Superconductivity in Low-Dimensional Systems