Hard-thermal-loop QED thermodynamics

Understand

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.