Renormalization of the 2PI-Hartree approximation in a broken phase with nonzero superflow

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.