  We show that the spectral function for single-particle excitations in a
two-dimensional Fermi liquid has Lorentzian shape in the low energy limit.
Landau quasi-particles have a uniquely defined spectral weight and a decay rate
which is much smaller than the quasi-particle energy. By contrast, perturbation
theory and the T-matrix approximation yield spurious deviations from Fermi
liquid behavior, which are particularly pronounced for a linearized dispersion
relation.
