  The momentum-shell renormalization group (RG) is used to study the
condensation of interacting Bose gases without and with disorder. First of all,
for the homogeneous disorder-free Bose gas the interaction-induced shifts in
the critical temperature and chemical potential are determined up to second
order in the scattering length. The approach does not make use of dimensional
reduction and is thus independent of previous derivations. Secondly, the RG is
used together with the replica method to study the interacting Bose gas with
delta-correlated disorder. The flow equations are derived and found to reduce,
in the high-temperature limit, to the RG equations of the classical
Landau-Ginzburg model with random-exchange defects. The random fixed point is
used to calculate the condensation temperature under the combined influence of
particle interactions and disorder.
