  We study a Bose-condensed gas at finite temperature, in which the particles
of the condensate and of the thermal cloud are constrained to move in a plane
under radial harmonic confinement and interact via strictly two-dimensional
collisions. The coupling parameters are obtained from a calculation of the
many-body T-matrix and decreases as temperature increases through a dependence
on the chemical potential and on the occupancy of excited states. We discuss
the consequences on the condensate fraction and on the density profiles of the
condensed and thermal components as functions of temperature, within a
simplified form of the two-fluid model.
