  Nonperturbative renormalization and explicit construction of the effective
potential of the Hartree approximation of the two-particle-irreducible
formalism are carried out in an inhomogeneous field configuration describing a
uniform superfluid. Based on the earlier article [G. Fejos et. al, Nucl. Phys.
A803, 115 (2008)], we clarify certain aspects of renormalizability
corresponding to the findings of [M. G. Alford et. al, Phys. Rev. D 89, 085005
(2014)]. We show that renormalizability of the approximation can be ensured by
regularization schemes respecting Lorentz and translation invariance.
Elimination of nonconventional superflow-dependent divergences is presented in
detail, together with a discussion on the finite-temperature treatment.
