Controlling a Non-Polynomial Reduced Finite Temperature Action in the U(1) Higgs Model

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.