We compute the critical temperature T_c of a weakly interacting uniform Bose
gas in the canonical ensemble, extending the criterion of condensation provided
by the counting statistics for the uniform ideal gas. Using ordinary
perturbation theory, we find in first order (Tc−Tc0)/Tc0=−0.93aρ1/3, where T_c^0 is the transition temperature of the corresponding
ideal Bose gas, a is the scattering length, and ρ is the particle number
density.Comment: 14 pages (RevTeX