Renormalization of self-consistent approximation schemes at finite temperature. II. Applications to the sunset diagram

Hees, Hendrik van; Knoll, J.

doi:10.1103/physrevd.65.105005

Cited by 142 publications

(235 citation statements)

References 18 publications

(43 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%

“…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.…”

Section: Motivationmentioning

confidence: 99%

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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%

Section: Motivationmentioning

confidence: 99%

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

2008

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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%

“…Within the CJT formalism, there are many attempts made to restore the Goldstone theorem in chiral limit, nevertheless, the existing approaches still could not provide a satisfactory solution to this long-standing problem [11,[22][23][24][25][26][27]. Very recently, Pilaftsis and Teresi have developed a novel symmetry improved CJT formalism by consistently encoding global symmetries in loop-wise expansions or truncations of the CJT effective action [28].…”

Section: Introductionmentioning

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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“…However solving the self-consistent equations of the BVA and constructing the thermal effective potential is a formidable task, and has only been recently considered for the simpler loop approximation to λφ 4 for the single field (N = 1) case (see Refs. [24,25]). Therefore in this paper, we consider the effective potential for the simpler Hartree approximation for a single field.…”

Section: Hartree Phase Diagrammentioning

confidence: 99%

Quantum dynamics of phase transitions in broken symmetryλφ4field theory

2003

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We perform a detailed numerical investigation of the dynamics of a single component broken symmetry λ φ 4 field theory in 1+1 dimensions using a Schwinger-Dyson equation truncation scheme based on ignoring vertex corrections. In an earlier paper, we called this the bare vertex approximation (BVA). We assume the initial state is described by a Gaussian density matrix peaked around some non-zero value of φ(0) , and characterized by a single particle Bose-Einstein distribution function at a given temperature. We compute the evolution of the system using three different approximations: Hartree, BVA and a related 2PI-1/N expansion, as a function of coupling strength and initial temperature. In the Hartree approximation, the static phase diagram shows that there is a first order phase transition for this system. As we change the initial starting temperature of the system, we find that the BVA relaxes to a new final temperature and exhibits a second order phase transition. We find that the average fields thermalize for arbitrary initial conditions in the BVA, unlike the behavior exhibited by the Hartree approximation, and we illustrate how φ(t) and χ(t) depend on the initial temperature and on the coupling constant. We find that the 2PI-1/N expansion gives dramatically different results for φ(t) .

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Renormalization of self-consistent approximation schemes at finite temperature. II. Applications to the sunset diagram

Cited by 142 publications

References 18 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

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

Quantum dynamics of phase transitions in broken symmetryλφ4field theory

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