2 PHASES OF TOPOLOGICALLY MASSIVE COMPACT U(1) THEORY

The mean-field-like gauge-invariant variational method formulated rece ntly is applied to topologically massive QED in three dimensions. We f ind that the theory has a phase transition in the Chern-Simons coeffic ient n. The phase transition is of the Berezinsky-Kosterlitz-Thouless type and is triggered by the liberation of Polyakov monopoles, which f or n>8 are tightly bound into pairs. In our Hamiltonian approach this is seen as a similar behavior of the magnetic vortices, which are pres ent in the ground state wave functional of the compact theory. For n>8 , the low energy behavior of the theory is the same as in the noncompa ct case. For n<8 there are no propagating degrees of freedom on distan ce scales larger than the ultraviolet cutoff. The distinguishing prope rty of the n<8 phase is that the magnetic flux symmetry is spontaneous ly broken.