Free energy of high temperature QED to order e5 from effective field theory

Massless quantum electrodynamics is studied at high temperature and zero chemical potential. We compute the Debye screening mass squared and the free energy to order e⁵ by an effective field theory approach, recently developed by Braaten and Nieto. Our results are in agreement with calculations done in resummed perturbation theory. This method makes it possible to separate contributions to the free energy from those to different momentum scales (order T and eT) and provides an economical alternative to computations in the full theory which involves the dressing of bosonic propagators.