The Finite Temperature s-Wave Superconductivity in the Two-Component Anyon Gas

onent anyon gas, and show that in the content of the BCS theory the long range gauge force can not be renormalized at the finite temperature T # 0, and this singularity is inherent and can not be overcome by adding other interactions of any form. We attribute this to the fake vortex excitations, and show that an elementary excitation over the supercondu&ive s-wave ground state in the two-component anyon gas is always in company with the excitation of a fake vortex. The finite temperature superconductivity in the two-component anyon gas is similar with the two-dimensional superfluid. There are two KT phase transitions.ponent anyon gas is similar with the two-dimensional superfluid. There are two KT phase transitions.