Effect of Interactions on the Critical Temperature of a Dilute Bose gas

Due to the observation of Bose-Einstein condensation in dilute atomic $^{87}$Rb and $^{23}$Na vapors last year, there is currently a great interest in the properties of a degenerate Bose gas. One aspect that is not yet understood is the effect of the interatomic interactions on the critical temperature of the phase transition. We present here a renormalization group study of the weakly-interacting Bose gas and predict the critical temperature at which Bose-Einstein condensation occurs as a function of the (positive) scattering length $a$ of the interatomic potential.