On the QED Effective Action in Time Dependent Electric Backgrounds

Gerald Dunne; Theodore Hall (U. Connecticut)

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On the QED Effective Action in Time Dependent Electric Backgrounds

Gerald Dunne, Theodore Hall (U. Connecticut)

High Energy Physics - Theory · Submitted 3 Jul 1998

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This expression is remarkably similar in form to Schwinger's classic result for the constant electric background.

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arXiv IDhep-th/9807031 (version 2)

Pith IDGKI5QEVA, Pith's permanent record of this paper and its review

CitationGerald Dunne, Theodore Hall (U. Connecticut). "On the QED Effective Action in Time Dependent Electric Backgrounds." arXiv:hep-th/9807031 (1998). https://pith.science/paper/GKI5QEVA

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What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.95 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We apply the resolvent technique to the computation of the QED effective action in time dependent electric field backgrounds. The effective action has both real and imaginary parts, and the imaginary part is related to the pair production probability in such a background. The resolvent technique has been applied previously to spatially inhomogeneous magnetic backgrounds, for which the effective action is real. We explain how dispersion relations connect these two cases, the magnetic case which is essentially perturbative in nature, and the electric case where the imaginary part is nonperturbative. Finally, we use a uniform semiclassical approximation to find an expression for very general time dependence for the background field. This expression is remarkably similar in form to Schwinger's classic result for the constant electric background.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We apply the resolvent technique to the computation of the QED effective action in time dependent electric field backgrounds.	contribution 0.79	0.95	0.07	asserted 1.00
s1	The effective action has both real and imaginary parts, and the imaginary part is related to the pair production probability in such a background.	background 0.86	0.18	0.08	asserted 1.00
s2	The resolvent technique has been applied previously to spatially inhomogeneous magnetic backgrounds, for which the effective action is real.	background 1.00	0.04	0.02	asserted 1.00
s3	We explain how dispersion relations connect these two cases, the magnetic case which is essentially perturbative in nature, and the electric case where the imaginary part is nonperturbative.	contribution 0.77	0.76	0.11	asserted 1.00
s4	Finally, we use a uniform semiclassical approximation to find an expression for very general time dependence for the background field.	method 0.63	0.96	0.21	asserted 1.00
s5	This expression is remarkably similar in form to Schwinger's classic result for the constant electric background.	result 0.80	0.89	0.41	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We apply the resolvent technique to the computation of the QED effective action in time dependent electric field backgrounds. The effective action has both real and imaginary parts, and the imaginary part is related to the pair production probability in such a background. The resolvent technique has been applied previously to spatially inhomogeneous magnetic backgrounds, for which the effective action is real. We explain how dispersion relations connect these two cases, the magnetic case which is essentially perturbative in nature, and the electric case where the imaginary part is nonperturbative. Finally, we use a uniform semiclassical approximation to find an expression for very general time dependence for the background field. This expression is remarkably similar in form to Schwinger's classic result for the constant electric background.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Resurgence of the Effective Action in Inhomogeneous Fields
hep-th 2022-12 unverdicted novelty 7.0 of 10

Inhomogeneous background fields convert Borel poles in the effective action to branch points and introduce new ones, allowing resurgent extrapolation to recover non-perturbative information from perturbative input mor...
QCD Vacuum in an Inhomogeneous Magnetic Field
hep-ph 2026-08 conditional novelty 6.0 of 10

In chiral perturbation theory, the QCD vacuum responds nonlocally to an inhomogeneous magnetic field, yielding parameter-free NLO predictions for the free energy, chiral condensate, and an induced vacuum current.
An Addendum to the Heisenberg-Euler effective action beyond one loop
hep-th 2016-12 accept novelty 6.0 of 10

The two-loop one-particle reducible term in the Heisenberg-Euler effective action is finite in constant fields, contradicting the standard assumption that it vanishes.
Worldline Instantons and Pair Production in Inhomogeneous Fields
hep-th 2005-07 accept novelty 6.0 of 10

Worldline instanton solutions show that temporal inhomogeneity of an electric field enhances vacuum pair production while spatial inhomogeneity suppresses it, matching prior WKB results.
Heisenberg-Euler Effective Lagrangians : Basics and Extensions
hep-th 2004-06 accept novelty 2.0 of 10

A pedagogical survey of Heisenberg-Euler effective Lagrangians, collecting the classic one-loop QED result, its expansions, and extensions to inhomogeneous, nonabelian and two-loop backgrounds.

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10 arXiv papers cite this in 10 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 5 sentences without a confident label

Compares with it 1 paper

The semiclassical results compare very well with these exact results in the semiclassical regime [ref] .

New Strong-Field QED Effects at ELI: Nonperturbative Vacuum Pair Production · The one-dimensional scattering picture · 0.88

Cites it as background 4 papers

Such investigations were undertaken in a series of works developing exact methods for evaluating quantum effective actions in solvable electromagnetic backgrounds [ref] .

QCD Vacuum in an Inhomogeneous Magnetic Field · Introduction · 0.83
Apart from this, higher-loop results in constant fields and lower space-time dimensions [ref] , as well as one-loop results for specific purely electric or magnetic (one-dimensional) field inhomogeneities are available [ref] .

Derivative corrections to the Heisenberg-Euler effective action · Introduction · 0.99
This can happen either thanks to some time-dependent potential [ref] (e.g. a scattering process or the Schwinger effect) or to some dynamical background geometry (e.g. an expanding universe [ref] or a collapsing black hole [ref] ).

Is the information loss problem a paradox? · Particle creation · 0.82

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