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Non-Fermi liquid behavior due to U(1) gauge field in two dimensions

We study the damping rate of massless Dirac fermions due to the U(1) gauge field in (2+1)-dimensional quantum electrodynamics. In the absence of a Maxwell term for the gauge field, the fermion damping rate $\mathrm{Im}Σ(ω,T)$ is found to diverge in both perturbative and self-consistent results. In the presence of a Maxwell term, there is still divergence in the perturbative results for $\mathrm{Im}Σ(ω,T)$. Once the Maxwell term is included into the self-consistent equations for fermion self-energy and vacuum polarization functions, the fermion damping rate is free of divergence and exhibits non-Fermi liquid behavior: $\mathrm{Im}Σ(ω,T) \propto \mathrm{max}(\sqrtω,\sqrt{T})$.