  Wilson's renormalization-group approach to the weakly-interacting
single-component Bose gas is discussed within the symmetry-broken, condensate
phase. Extending upon the work by Bijlsma and Stoof [Phys. Rev. A 54, 5085
(1996), see http://doi.org/10.1103/PhysRevA.54.5085 ], wave-function
renormalization of the temporal derivative contributions to the effective
action is included in order to capture sound-like quasiparticle excitations
with wave lengths larger than the healing-length scale. By means of a suitable
rescaling scheme we achieve convergence of the coupling flows, which serve as a
means to determine the condensate depletion in accordance with Bogoliubov
theory, as well as the interaction-induced shift of the critical temperature.
