  In general the zero momentum limit of thermal self-energies calculated in
perturbation theory depends on the order in which the time and the space
components of the momentum are taken to zero. We show that this is an artifact
of the perturbative calculation, and in fact the non-analyticity of the
one-loop self-energy disappears when it is calculated with improved vertices
and/or improved propagators that incorporate the imaginary part of the
self-energy.
