PUB - Publikationen an der Universität Bielefeld

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