Derivation of Asymptotic Expansions

Dingle, R.

doi:10.1038/196849b0

Cited by 63 publications

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“…WKB analysis of the Stokes phenomenon is one of the common semi-classical methods. There are several variants of this method, e.g., the phase-integral method [662][663][664][665] and the divergent asymptotic series method [337,647,666]. We shall review this method in the language of exact WKB [649][650][651][652].…”

Section: Theoretical Framework 811 Semi-classical Methods and The Sto...mentioning

confidence: 99%

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Advances in QED with intense background fields

et al. 2023

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Section: Theoretical Framework 811 Semi-classical Methods and The Sto...mentioning

confidence: 99%

“…The function F j is called singulant [337,666]. The advantage of the superadiabatic particle number is that it connects the asymptotic numbers of created pairs very smoothly and does not show unpleasant oscillations and peaks observed with the WKB mode functions (see Fig.…”

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Advances in QED with intense background fields

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“…arises in many contexts, A is referred to by various names. We will follow Dingle and refer to is as the singulant [100]. In the case of MIS theory A = 3/2C τ Π , which shows that the divergence originates in the nonhydrodynamic sector.…”

Section: The Gradient Expansion At Large Ordersmentioning

confidence: 99%

Constraining the initial stages of ultrarelativistic nuclear collisions

et al. 2021

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One of the many physical questions that have emerged from studies of heavy-ion collisions at RHIC and the LHC concerns the validity of hydrodynamic modelling at the very early stages, when the Quark-Gluon Plasma system produced is still far from isotropy.In this article we review the idea of far-from-equilibrium hydrodynamic attractors as a way to understand how the complexity of initial states of nuclear matter is reduced so that a hydrodynamic description can be effective.

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“…As it is known from the early 50s [2], these amplitudes are not regular functions at α = 0 , irrelevant to the existence of UV divergencies and renormalization. The most general and transparent argument [3] can be formulated via a representation of path integral.…”

Section: Subject and Motivationmentioning

confidence: 99%

Novel sets of coupling expansion parameters for low-energy pQCD

Shirkov

2008

Phys. Part. Nuclei Lett.

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In quantum theory, physical amplitudes are usually presented in the form of Feynman perturbation series in powers of coupling constant α . However, it is known that these amplitudes are not regular functions at α = 0 .For QCD, we propose new sets of expansion parameters w k (α s ) that reflect singularity at α s = 0 and should be used instead of powers α k s . Their explicit form is motivated by the so called Analytic Perturbation Theory. These parameters reveal saturation in a strong coupling case at the level α ef f s (α s ≫ 1) = w 1 (α s ≫ 1) ∼ 0.5 . They can be used for quanitative analysis of divers low-energy amplitudes.We argue that this new picture with non-power sets of perturbation expansion parameters, as well as the saturation feature, is of a rather general nature.1 A preliminary version with the main results was published in Ref. [1].

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Derivation of Asymptotic Expansions

Cited by 63 publications

References 0 publications

Advances in QED with intense background fields

Advances in QED with intense background fields

Constraining the initial stages of ultrarelativistic nuclear collisions

Novel sets of coupling expansion parameters for low-energy pQCD

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