Renormalization of fermion velocity in finite temperature QED_{3}

TL;DR

This paper investigates how finite temperature affects fermion velocity in 3D quantum electrodynamics, revealing that transverse gauge interactions cause an unusual velocity renormalization due to broken Lorentz invariance.

Contribution

It provides a renormalization group analysis of fermion velocity at finite temperature, highlighting the impact of transverse gauge interactions and Lorentz invariance breaking.

Findings

Fermion velocity is renormalized by transverse gauge interactions at finite temperature.

Long-ranged transverse gauge interactions lead to singular self-energy corrections.

The anomalous dimension influences the fermion specific heat.

Abstract

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.