PUB - Publikationen an der Universität Bielefeld

We calculate the free energy of a hot gas of electrons and photons to threeloops using the hard-thermal-loop perturbation theory reorganization offinite-temperature perturbation theory. We calculate the free energy throughthree loops by expanding in a power series in m_D/T, m_f/T, and e^2, where m_Dand m_f are thermal masses and e is the coupling constant. We demonstrate thatthe hard-thermal-loop perturbation reorganization improves the convergence ofthe successive approximations to the QED free energy at large coupling, e ~ 2.The reorganization is gauge invariant by construction, and due to cancellationamong various contributions, we obtain a completely analytic result for theresummed thermodynamic potential at three loops. Finally, we compare our resultwith similar calculations that use the Phi-derivable approach.