The ε expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature

We discuss the application of the momentum-shell renormalization group method to the interacting homogeneous Bose gas in the symmetric and symmetry-broken phases. It is demonstrated that recently discussed discrepancies are artefacts due to not taking proper care of infrared divergencies appearing at finite temperature. If these divergencies are taken into account and treated properly by means of the ε expansion, the resulting renormalization group equations and the corresponding universal properties are identical in the symmetric and symmetry-broken phases.