Hard-thermal-loop QED thermodynamics

TL;DR

This paper applies hard-thermal-loop perturbation theory to compute the thermodynamic free energy of QED at three-loop order, demonstrating improved convergence and gauge invariance at moderate coupling strengths.

Contribution

It presents a three-loop calculation of QED thermodynamics using HTLpt, providing an analytic, gauge-invariant resummed result that enhances convergence at larger couplings.

Findings

Improved convergence of free energy calculations at e ~ 2

Analytic, gauge-invariant three-loop thermodynamic potential

Demonstration of HTLpt effectiveness at moderate coupling

Abstract

The weak-coupling expansion for thermodynamic quantities in thermal field theories is poorly convergent unless the coupling constant is tiny. We discuss the calculation of the free energy for a hot gas of electrons and photons to three-loop order using hard-thermal-loop perturbation theory (HTLpt). We show that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e ~ 2. The reorganization is gauge invariant by construction, and due to the cancellations among various contributions, we obtain a completely analytic result for the resummed thermodynamic potential at three loops.