ABELIAN VERSUS NON-ABELIAN HIGGS-MODEL IN 3 DIMENSIONS

We study the phase structure of the abelian Higgs model in three dimen sions based on perturbation theory and a set of gauge independent gap equations for Higgs boson and vector boson masses. Contrary to the non -abelian Higgs model, the vector boson mass vanishes in the symmetric phase. In the Higgs phase the gap equations yield masses consistent wi th perturbation theory. The phase transition is first-order for small values of the scalar self-coupling lambda, where the employed loop exp ansion is applicable.