Due to tile observation of Bose-Einstein condensation in dilute atomic
Rb-87, Li-7, and Na-23 vapors last year, there is currently a great i
nterest in tile degenerate dilute Dose gas. Existing theoretical appro
aches using basically non-interacting Bogoliubov quasi-particles do no
t predict the deviation from the ideal gas critical temperature claime
d to be observed in tile experiments. Improving the theoretical analys
is by including interactions between the Bogoliubov quasi-particles is
however not trivial in the degenerate regime due to infrared divergen
cies showing up in regular perturbation theory. Motivated by these asp
ects we present a renormalization group study of tile weakly-interacti
ng homogeneous Bose gas.