Renormalization of fermion velocity in finite temperature QED₃

At zero temperature, the Lorentz invariance is strictly preserved in three-dimensional quantum electrodynamics. This property ensures that the velocity of massless fermions is not renormalized by the gauge interaction. At finite temperature, however, the Lorentz invariance is explicitly broken by the thermal fluctuation. The longitudinal component of gauge interaction becomes short-ranged due to thermal screening, whereas the transverse component remains long-ranged because of local gauge invariance. The transverse gauge interaction leads to singular corrections to the fermion self-energy and thus results in an unusual renormalization of the fermion velocity. We calculate the renormalized fermion velocity $v^R(p_0,\mathbf{p},T)$ by employing a renormalization group analysis, and discuss the influence of the anomalous dimension $\eta_n$ on the fermion specific heat.