Renormalization of Φ-derivable approximations in scalar field theories

Blaizot, Jean‐Paul; Iancu, Edmond; Reinosa, Urko

doi:10.1016/j.nuclphysa.2004.02.019

Cited by 115 publications

(148 citation statements)

References 29 publications

(61 reference statements)

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“…Another interesting direction will be to see to what extent the proposed single-step procedure can be incorporated in the renormalisation of the momentum-dependent truncations of the 2PI approximation recently studied in [9,1,10,31].…”

Section: Discussionmentioning

confidence: 99%

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

2008

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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 one-and two-point functions. The non-perturbative counterterms are deduced from the conditions for the cancellation of the overall and the subdivergences in the complete Hartree-Dyson-Schwinger equations, with a transparent method. The procedure proposed in the present paper is shown to be equivalent to the iterative renormalisation method of Blaizot et al.[1]. MotivationOne of the most popular approximation techniques in many-body quantum theory is the Hartree approximation. In quantum field theory it corresponds to the momentum independent two-loop truncation of the two-particle irreducible effective action. It is used extensively both in equilibrium [2,3,4] and out-of-equilibrium [5,6,7,8] non-perturbative investigations of phase transition phenomena. Its non-perturbative renormalisability was demonstrated as particular case of the general proof of renormalisability of the physical quantities computed in various 2PI approximations [9,1,10]. These proofs are rather involved especially in the broken symmetry phase. For this reason in many practical applications the renormalised equations are not constructed explicitly. For instance, investigations of the finite temperature phase transitions in strongly interacting matter frequently either omit zero temperature quantum corrections in the 2PI approximate equations of the relevant 1-and 2-point functions [3,4,11] or take into account vacuum fluctuations by applying some cut-off [12].The exact generating 2PI-functional Γ[Φ, G] fulfils generalised Ward-Takahashi identities reflecting global internal symmetries of the models. As a consequence the 1PI effective potential Γ[Φ, G(Φ)]

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Section: Discussionmentioning

confidence: 99%

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

2008

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“…It has been shown in [32][33][34] that the 2PI formalism is renormalizable with T -independent CTs. In order to determine the latter, we follow an alternative method similar to [35], which does not involve considering a Bethe-Salpeter equation.…”

Section: Renormalizationmentioning

confidence: 99%

Symmetry-improved CJT effective action

2013

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The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward identities due to global symmetries. By considering a simple O(2) scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O (2) is massless and the phase transition is a second order one, already in the Hartree-Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree-Fock approximated CJT effective action, we calculate the corresponding symmetryimproved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.

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“…Renormalization in many-body approximation schemes is a nontrivial procedure, and this problem has been extensively discussed in Refs. [24,[34][35][36]. In the following discussions, we follow the "counter term" renormalization scheme (CT) adopted in Ref.…”

Section: The Effective Potential In the Symmetry Improved Cjt Fomentioning

confidence: 99%

“…In order to analyze the order of phase transition, in the spontaneous symmetry breaking phase, that is φ = 0, from the gap equations (33) and the relationship in Eqs. (34), the chiral condensate φ can be described as…”

Section: Comparison With Large-n Approximationmentioning

confidence: 99%

On the symmetry improved CJT formalism in the O(4) linear sigma model

Mao

2014

Nuclear Physics A

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By using the symmetry improved CJT effective formalism developed by Pilaftsis and Teresi, the chiral phase transition is reconsidered in the framework of the O(4) linear sigma model in chiral limit. Our results confirm the restorations of the second-order phase transition and the Goldstone theorem in the Hartree approximation. Finally, we explicitly calculate the effective potentials via the order parameter for various temperatures and address advantages of the present method in comparison with the O(N ) model in large-N approximation.

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Renormalization of Φ-derivable approximations in scalar field theories

Cited by 115 publications

References 29 publications

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

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

Symmetry-improved CJT effective action

On the symmetry improved CJT formalism in the O(4) linear sigma model

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