QED Thermodynamics at Intermediate Coupling

TL;DR

This paper applies hard-thermal-loop perturbation theory to QED at intermediate coupling, demonstrating improved convergence and gauge invariance in calculating the free energy at three loops.

Contribution

It introduces a three-loop HTL-improved approximation for QED free energy, showing enhanced convergence and analytic results at intermediate coupling.

Findings

Improved convergence of perturbative series at e ~ 2

Gauge-invariant resummation yields analytic thermodynamic potential

Successful application of HTL perturbation at three-loop order

Abstract

We discuss reorganizing finite temperature perturbation theory using hard-thermal-loop (HTL) perturbation theory in order to improve the convergence of successive perturbative approximations to the free energy of a gauge theory. We briefly review the history of the technique and present new results for the three-loop HTL-improved approximation for the free energy of QED. We show that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at intermediate coupling, e ~ 2. The reorganization is gauge invariant by construction, and due to cancellation among various contributions, one can obtain a completely analytic result for the resummed thermodynamic potential at three loops.