  The effect of ordering field phase fluctuations on the normal and
superconducting properties of a simple 2D model with a local four-fermion
attraction is studied. Neglecting the coupling between the spin and charge
degrees of freedom an analytical expression has been obtained for the fermion
spectral function as a single integral over a simple function. From this we
show that, as the temperature increases through the 2D critical temperature and
a nontrivial damping for a phase correlator develops, quantum fluctuations fill
the gap in the quasiparticle spectrum. Simultaneously the quasiparticle peaks
broaden significantly above the critical temperature, resembling the observed
pseudogap behavior in high-T_c superconductors.
