Improved Hartree--Fock resummations and spontaneous symmetry breaking

Abstract

The standard Hartree--Fock approximation of the $O(N)-$invariant ${\varphi }^4$ model suffers from serious renormalization problems. In addition, when the symmetry is spontaneously broken, another shortcoming appears in relation to the Goldstone bosons: they fail to be massless in the intermediate states. In this work, within the framework of out--of--equilibrium Quantum Field Theory, we propose a class of systematic improvements of the Hartree--Fock resummation which overcomes all the above mentioned difficulties while ensuring also exact Renormalization--Group invariance to one loop.

42 pages, 9 figures

References in corpus (11)

• Introduction to Nonequilibrium Quantum Field Theory
• Nonperturbative renormalization for 2PI effective action techniques
• Gapless Hartree-Fock Resummation Scheme for the O(N) Model
• Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $\lambda {\varphi }^4$ field theory
• Progress in nonequilibrium quantum field theory III
• Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model
• Renormalization of a gapless Hartree-Fock approximation to a theory with spontaneously broken O(N)-symmetry
• The renormalized and Renormalization-Group invariant Hartree-Fock approximation
• O(N) linear sigma model beyond the Hartree approximation at finite temperature
• Nonequilibrium dynamics of the O(N) linear sigma model
• Renormalization and resummation in field theories

Cited by in corpus (1)

• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase