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Ivanov, Yu. B.; Riek, F.; Knoll, J.

doi:10.1103/physrevd.71.105016

Cited by 55 publications

(102 citation statements)

References 42 publications

(65 reference statements)

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“…Consequently, within our symmetry-improved CJT formalism, we predict a second-order phase transition already in the HF approximation, in agreement with theoretical expectations to all orders. This should be contrasted with the first-order phase-transition predicted in the HF approximation by the existing approaches [13,14,16].…”

Section: Uv Finite Solutions To Renormalized Gap Equationsmentioning

confidence: 99%

“…In particular, for the case of global O(N ) symmetries that we will be studying here, a naive truncation of the CJT effective action violates the Goldstone theorem [7,8] by higher-order terms, giving rise to a massive Goldstone boson in the Spontaneous Symmetry Breaking (SSB) phase of the theory [9][10][11][12]. Thus far, several studies have been presented in the literature, attempting to provide a satisfactory solution to this problem [11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…A first attempt in restoring the Goldstone theorem within the CJT formalism was to add a phenomenological term to the 2PI effective action [13,14]. In the HF approximation, such an approach has as major drawback.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Uv Finite Solutions To Renormalized Gap Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Symmetry-improved CJT effective action

2013

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“…We will shortly comment on the counter term structure of the "symmetrized" approximate 2PI-Hartree functional of Ref. [15] in the present scheme. In section 3 we introduce the general class of the models we shall investigate and write the truncated expression of their effective quantum action corresponding to the Hartree-approximation.…”

Section: Motivationmentioning

confidence: 99%

“…this approximation does not lead to a thermalised symmetry breaking ground state [14]. Recently a "symmetrized" modification was proposed to replace the original 2PI-functional, which can be uniquely constructed from the requirement of obeying Goldstone's theorem [15].…”

Section: Motivationmentioning

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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