Improved Hartree--Fock resummations and spontaneous symmetry breaking

The standard Hartree-Fock approximation of the O(N)-invariant Ï•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. © 2006 The American Physical Society.