We consider the Bose-Einstein transition of homogeneous weakly interactingspin-0 particles based on the normal-state Phi-derivable approximation.Self-consistent calculations of Green's function and the chemical potentialwith several approximate Phi's are performed numerically as a function oftemperature near Tc, which exhibit qualitatively different results. The ladderapproximation apparently shows a continuous transition with the prefactorc=2.94 for the transition-temperature shift given in terms of the scatteringlength a and density n. In contrast, the second-order, particle-hole, andfluctuation-exchange approximations yield a first-order transition. The factthat some standard Phi's predict a first-order transition challenges us toclarify whether or not the transition is really continuous.
展开▼
