Related papers: Gapless Hartree-Fock Resummation Scheme for the O(…
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…
The standard Hartree--Fock approximation of the $O(N)-$invariant $\phi^4$ model suffers from serious renormalization problems. In addition, when the symmetry is spontaneously broken, another shortcoming appears in relation to the Goldstone…
We study the linear sigma model with O(N) symmetry at nonzero temperature in the framework of the Cornwall-Jackiw-Tomboulis formalism. Extending the set of two-particle irreducible diagrams by adding sunset diagrams to the usual…
We study the renormalization problem for the Hartree--Fock approximation of the $O(N)-$invariant $\phi^4$ model in the symmetric phase and show how to systematically improve the corresponding diagrammatic resummation to achieve the correct…
The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the $\phi^4$-theory. Besides the tadpole (Hartree) approximation as a…
We apply a self-consistent relativistic mean-field variational ``Gaussian functional'' (or Hartree) approximation to the linear $\sigma$ model with spontaneously and explicitly broken chiral O(4) symmetry. We set up the self-consistency, or…
The spontaneous symmetry breaking in noncommutative $\lambda\Phi^4$ theory has been analyzed by using the formalism of the effective action for composite operators in the Hartree-Fock approximation. It turns out that there is no phase…
We discuss the thermodynamics of the O(N) model across the corresponding phase transition using the two-loop Phi-derivable approximation of the effective potential and compare our results to those obtained in the literature within the…
We study the O(N) linear sigma model with spontaneous symmetry breaking, using a Hartree-like ansatz with a classical field and variational masses. We go beyond the Hartree approximation by including the two-loop contribution, the sunset…
We present a self--consistent solution of the finite temperature gap--equation for $\lambda \Phi^4$ theory beyond the Hartree-Fock approximation using a composite operator effective action. We find that in a spontaneously broken theory not…
The optimized perturbation theory (OPT) at finite temperature recently developed by the present authors is reviewed by using O(N) phi^4 theory with spontaneous symmetry breaking. The method resums automatically higher loops (including the…
We study the O(N) linear sigma model with spontaneous symmetry breaking at finite temperature in the framework of the two-particle point-irreducible (2PPI) effective action. We go beyond the Hartree approximation by including the two-loop…
We show that a new expansion which sums seagull and bubble graphs to all orders, can be applied to the O(N) linear sigma model at finite temperature. We prove that this expansion can be renormalised with the usual counterterms in a mass…
We derive the renormalized Schwinger-Dyson equations for the one- and two-point functions in the auxiliary field formulation of $\lambda \phi^4$ field theory to order 1/N in the 2PI-1/N expansion. We show that the renormalization of the…
The autonomous renormalization of the O(N)-symmetric scalar theory is based on an infinite re-scaling of constant fields, whereas finite-momentum modes remain finite. The natural framework for a detailed analysis of this method is a system…
An optimized perturbation theory (OPT) at finite temperature T, which resums higher order terms in the naive perturbation, is developed in O(N) phi^4 theory. It is proved that (i) the renormalization of the ultra-violet divergences can be…
Explicit counterterm construction is presented in a symmetry breaking background for the 2PI effective action of the self-interacting one-component scalar field including skeleton diagrams to O(\lambda^2). The applied strategy is an…
Non-perturbative renormalisation of a general class of scalar field theories is performed at the Hartree level truncation of the 2PI effective action in the broken symmetry regime. Renormalised equations are explicitly constructed for the…
The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N…
We study the effective potential of a real scalar phi^4 theory as a function of the temperature T within the simplest Phi-derivable approximation, namely the Hartree approximation. We apply renormalization at a "high" temperature T* where…