Two-dimensional dilute Bose gas in the normal phase

We consider a two-dimensional dilute Bose gas above its superfluid transition temperature. We show that the t-matrix approximation corresponds to the leading set of diagrams in the dilute limit, provided the temperature is sufficiently larger than the superfluid transition temperature. Within this approximation, we give an explicit expression for the wave-vector and frequency dependence of the self-energy, and calculate the corrections to the chemical potential and the effective mass arising from the interaction. We also argue that the breakdown of diagrammatic classification scheme for the dilute Bose gas, which occurs upon lowering the temperature, provides a criterion to estimate an upper bound for the superfluid critical temperature. The tipper bound to the critical temperature identified by this criterion turns out to coincide with earlier results for the critical temperature obtained by Popov and by, Fisher and Hohenberg using different methods. Extension of this procedure to the three-dimensional case gives good agreement with recent Monte Carlo data.