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

TL;DR

This paper addresses the nonperturbative renormalization of the 2PI-Hartree approximation in a superfluid phase, ensuring renormalizability through Lorentz-invariant regularization and discussing finite-temperature effects.

Contribution

It provides a detailed explicit construction of the effective potential and clarifies renormalizability conditions for the 2PI-Hartree approximation in inhomogeneous superfluid configurations.

Findings

Renormalizability is maintained with Lorentz-invariant regularization schemes.

Superflow-dependent divergences can be eliminated explicitly.

Finite-temperature effects are discussed in the context of the approximation.

Abstract

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.