Effect of weak interactions on the ultrarelativistic Bose-Einstein condensation temperature

We calculate the ultrarelativistic Bose-Einstein condensation temperature of a complex scalar field with weak lambda(Phi (dagger)Phi)(2) interaction. We show that at high temperature and finite density we can use dimensional reduction to produce an effective three-dimensional theory which then requires nonperturbative analysis. For simplicity and ease of implementation we illustrate this process with the linear delta expansion.