Renormalization of a gapless Hartree-Fock approximation to a theory with   spontaneously broken O(N)-symmetry
  The renormalization of a gapless Phi-derivable Hartree--Fock approximation to the O(N)-symmetric lambda*phi^4 theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper in order to preserve all the desirable features of Phi-derivable Dyson-Schwinger resummation schemes (i.e., validity of conservation laws and thermodynamic consistency) while simultaneously restoring the Nambu--Goldstone theorem in the broken phase. It is shown that unlike for the conventional Hartree--Fock approximation this approach allows for a scale-independent renormalization in the vacuum. However, the scale dependence still persists at finite temperatures. Various branches of the solution are studied. The occurrence of a limiting temperature inherent in the renormalized Hartree--Fock approximation at fixed renormalization scale mu is discussed. 
Yu. B. Ivanov (1 and 2), F. Riek (1), H. van Hees (3), J. Knoll (1)   ((1) GSI Darmstadt, (2) Kurchatov Institute Moscow, (3...