QED is studied at low temperature (T≪m, where m is the electron mass)
and zero chemical potential. By integrating out the electron field and the
nonzero bosonic Matsubara modes, we construct an effective three-dimensional
field theory that is valid at distances R≫1/T. As applications, we
reproduce the ring-improved free energy and calculate the Debye mass to order
e5.Comment: 20 pages, 4 figures, revte