  An effective theory is constructed for the scalar electrodynamics via 2-loop
integration over all non-static fields and the screened electric component of
the vector-potential. Non-polynomial terms of the action are preserved and
included into the 2-loop calculation of the effective potential of the reduced
theory. Also the inclusion of some non-local terms is shown to be important.
The effect of non-polynomial operators on the symmetry restoring phase
transition is quantitatively compared to results from a local,
superrenormalisable approximate effective theory.
