Borel summation of the derivative expansion and effective actions

Dunne, Gerald V.; Hall, Theodore

doi:10.1103/physrevd.60.065002

Cited by 76 publications

(101 citation statements)

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“…It shows that from a knowledge of the large order divergence behavior (2.3) of the perturbative expansion, we can deduce non-perturbative information about the imaginary part of the effective Lagrangian density, under the assumption that no other Borel poles or cuts contribute. In certain cases one can even extend this analysis to inhomogeneous background fields, with the derivative expansion capturing non-perturbative information in its divergence [31]. These results provide a working illustration of Dyson's formal physical argument [32] concerning the divergence of QED perturbation theory: one can argue that the weak-field expansions (2.2) and (2.6) could not be convergent, because if they were, they could not capture the genuine non-perturbative effect of pair production.…”

Section: Scalar Effective Action In Electromagnetic Backgroundsmentioning

confidence: 99%

Large-order perturbation theory and de Sitter/anti–de Sitter effective actions

Das

Dunne

2006

Phys. Rev. D

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We analyze the large-order behavior of the perturbative weak-field expansion of the effective Lagrangian density of a massive scalar in de Sitter and anti de Sitter space, and show that this perturbative information is not sufficient to describe the non-perturbative behavior of these theories, in contrast to the analogous situation for the Euler-Heisenberg effective Lagrangian density for charged scalars in constant electric and magnetic background fields. For example, in even dimensional de Sitter space there is particle production, but the effective Lagrangian density is nevertheless real, even though its weak-field expansion is a divergent non-alternating series whose formal imaginary part corresponds to the correct particle production rate. This apparent puzzle is resolved by considering the full non-perturbative structure of the relevant Feynman propagators, and cannot be resolved solely from the perturbative expansion. * Electronic address: das@pas.rochester.edu † Electronic address: dunne@phys.uconn.edu

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Section: Scalar Effective Action In Electromagnetic Backgroundsmentioning

confidence: 99%

Large-order perturbation theory and de Sitter/anti–de Sitter effective actions

Das

Dunne

2006

Phys. Rev. D

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“…Moreover, this system is known to be WKB-exact [26,24]. Then when the momentum integrals in (22) are done, we obtain precisely the leading results (17) or (20), depending on whether we are in the "non-perturbative" eEτ m ≫ 1, or "perturbative" eEτ m ≪ 1 regime [15]. This serves as a useful cross-check of our Borel analysis.…”

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confidence: 94%

“…However, we can avoid both these problems at once by considering some special exactly solvable cases [15]. In these cases, the background inhomogeneity can be characterized by a single scale parameter, so that the derivative expansion becomes a true series, in inverse powers of this scale parameter.…”

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confidence: 99%

“…It is an instructive exercise to apply this Borel technology to the alternating divergent Euler-Heisenberg effective action (5) [15][16][17]. Combining the asymptotic form (6) of the coefficients with the Borel formula (10) we obtain…”

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confidence: 99%

“…But the situation is even more interesting than this result (17) suggests. For example, we could instead have considered doing the Borel resummation for the j summations, at each fixed k. Then for large j, the coefficients behave as [15] a (k)…”

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QED effective actions in inhomogeneous backgrounds: Summing the derivative expansion

Dunne¹

2001

AIP Conference Proceedings

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Abstract. The QED effective action encodes nonlinear interactions due to quantum vacuum polarization effects. While much is known for the special case of electrons in a constant electromagnetic field (the Euler-Heisenberg case), much less is known for inhomogeneous backgrounds. Such backgrounds are more relevant to experimental situations. One way to treat inhomogeneous backgrounds is the "derivative expansion", in which one formally expands around the soluble constant-field case. In this talk I use some recent exactly soluble inhomogeneous backgrounds to perform precision tests on the derivative expansion, to learn in what sense it converges or diverges. A closely related question is to find the exponential correction to Schwinger's pair-production formula for a constant electric field, when the electric background is inhomogeneous.This talk is concerned with the one-loop QED effective action [1,2]:Here D µ = ∂ µ + ieA µ is the covariant derivative, and so S[A] is a functional of the classical background field A µ (x). The effective action is the generating functional for one-fermion-loop Green's functions, which describe the nonlinear QED effects to this order. Ideally, one would like to know S[A] for any field A µ (x), but this is not feasible. However, for the special case where the field strength tensor, F µν = ∂ µ A ν − ∂ ν A µ , is uniform, the effective action can be evaluated in closed form [3][4][5]:Here the first term is the familiar classical Maxwell action, while the next term gives the leading quantum correction, which is quartic in the field strengths. The fine structure constant α = e 2 4π in these units. All higher terms in the expansion (2) are known explicitly [3][4][5]. It can also be shown that when the background field is a constant electric field of strength E, the effective action has an exponentially small imaginary part

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In-Out Formalism for One-Loop Effective Actions in QED and Gravity

Kim

2017

Russ Phys J

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The in-out formalism is a systematic and powerful method for finding the effective actions in an electromagnetic field and a curved spacetime provided that the field equation has explicitly known solutions. The effective action becomes complex when pairs of charged particles are produced due to an electric field and curved spacetime. This may lead to a conjecture of one-to-one correspondence between the vacuum polarization (real part) and the vacuum persistence (imaginary part). We illustrate the one-loop effective action in a constant electric field in a Minkowski spacetime and in a uniform electric field in a two-dimensional (anti-) de sitter space.Comment: Latex 7 pages; contribution to the Workshop Proceedings of the International Workshop SFP-2016: Strong Field Problems in Quantum Theory, Tomsk, Russia, June 6-11, 201

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Borel summation of the derivative expansion and effective actions

Cited by 76 publications

References 47 publications

Large-order perturbation theory and de Sitter/anti–de Sitter effective actions

Large-order perturbation theory and de Sitter/anti–de Sitter effective actions

QED effective actions in inhomogeneous backgrounds: Summing the derivative expansion

In-Out Formalism for One-Loop Effective Actions in QED and Gravity

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