Spectral function of two-dimensional Fermi liquids

We show that the spectral function for single-particle excitations in a two-dimensional Fermi liquid has a Lorentzian shape in the low-energy limit. Landau quasiparticles have a uniquely defined spectral weight and a decay rate which is much smaller than the quasiparticle 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.