Convergence of Scaled Delta Expansion: Anharmonic Oscillator

Guida, Riccardo; Konishi, Kenichi; Suzuki, Hiroshi

doi:10.1006/aphy.1995.1059

Cited by 98 publications

(177 citation statements)

References 13 publications

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“…(More precisely, for asymptotically free theories, the optimized mass is automatically of the order of the basic scale Λ ∼ µ e −1/(b0 g) , in contrast with the original vanishing mass). In simpler (D = 1) models the procedure may be seen as a particular case of "order-dependent mapping" [27], which has been proven [28] to converge exponentially fast for the D = 1 Φ 4 oscillator energy levels. For higher dimensional D > 1 renormalizable models, the behavior at large orders in δ is more involved, and no rigorous convergence proof exists, although OPT was shown to partially damp the factorially divergent (infrared renormalons) perturbative behavior at large orders [29].…”

Section: Optimized and Rg Optimized Perturbation (Rgopt)mentioning

confidence: 99%

Chiral condensate from renormalization group optimized perturbation

Kneur

Neveu

2015

Phys. Rev. D

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Our recently developed variant of variationnally optimized perturbation (OPT), in particular consistently incorporating renormalization group properties (RGOPT), is adapted to the calculation of the QCD spectral density of the Dirac operator and the related chiral quark condensate qq in the chiral limit, for n f = 2 and n f = 3 massless quarks. The results of successive sequences of approximations at two-, three-, and four-loop orders of this modified perturbation, exhibit a remarkable stability. We obtain qq 1/3 n f =2 (2 GeV) = −(0.833 − 0.845)Λ2, and qq 1/3 n f =3 (2 GeV) = −(0.814 − 0.838)Λ3 where the range spanned by the first and second numbers (respectively fourand three-loop order results) defines our theoretical error, andΛn f is the basic QCD scale in the M S-scheme. We obtain a moderate suppression of the chiral condensate when going from n f = 2 to n f = 3. We compare these results with some other recent determinations from other nonperturbative methods (mainly lattice and spectral sum rules).

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Section: Optimized and Rg Optimized Perturbation (Rgopt)mentioning

confidence: 99%

Chiral condensate from renormalization group optimized perturbation

Kneur

Neveu

2015

Phys. Rev. D

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“…Later, the rigorous convergence proof of ODM was given [6] for g > g 0 ≃ 0.1, where g 0 is the convergence radius of the strong coupling expansion.…”

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confidence: 99%

“…However it cannot take the place of the semi-classical approximation because it fails in the weak coupling regime g < 0.1. This is unsatisfactory although the failure can be understood [6] as the effect of Bender-Wu singularity [1] on the higher Riemann surface. As the another displeased feature of ODM, the method just gives a "number," which is a solution of a higher algebraic equation, hence does not allow a simple analytical characterization such as (2).…”

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confidence: 99%

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Observing quantum tunneling in perturbation series

Suzuki

Yasuta

1997

Physics Letters B

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We apply Borel resummation method to the conventional perturbation series of ground state energy in a metastable potential, V (x) = x 2 /2 − gx 4 /4. We observe numerically that the discontinuity of Borel transform reproduces the imaginary part of energy eigenvalue, i.e., total decay width due to the quantum tunneling.The agreement with the exact numerical value is remarkable in the whole tunneling regime 0 < g < 0.7.

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“…It is considered as a sort of variational method [13,14,15,16,17,18]. It has been successfully applied to various models [19,20,21,22], and applications to matrix models were done in Refs. [23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Improved perturbation method and its application to the IIB matrix model

Aoyama

Shibusa

2006

Nuclear Physics B

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We present a new scheme for extracting approximate values in "the improved perturbation method", which is a sort of resummation technique capable of evaluating a series outside the radius of convergence.We employ the distribution profile of the series that is weighted by nth-order derivatives with respect to the artificially introduced parameters. By those weightings the distribution becomes more sensitive to the "plateau" structure in which the consistency condition of the method is satisfied. The scheme works effectively even in such cases that the system involves many parameters. We also propose that this scheme has to be applied to each observable separately and be analyzed comprehensively.We apply this scheme to the analysis of the IIB matrix model by the improved perturbation method obtained up to eighth order of perturbation in the former works. We consider here the possibility of spontaneous breakdown of Lorentz symmetry, and evaluate the free energy and the anisotropy of space-time extent. In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)-and SO(7)-symmetric vacua that have been observed. It is also found that there are two distinct SO(4)-symmetric vacua that have almost the same value of free energy but the extent of space-time is different. From the approximate values of free energy, we conclude that the SO(4)-symmetric vacua are most preferred among those three types of vacua.

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Convergence of Scaled Delta Expansion: Anharmonic Oscillator

Cited by 98 publications

References 13 publications

Chiral condensate from renormalization group optimized perturbation

Chiral condensate from renormalization group optimized perturbation

Observing quantum tunneling in perturbation series

Improved perturbation method and its application to the IIB matrix model

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