An All-Orders Derivative Expansion

Dunne, Gerald V.

doi:10.1142/s0217751x97000876

Cited by 14 publications

(22 citation statements)

References 13 publications

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“…These results provide strong evidence that the expansion (33) of the exact result is an all-orders derivative expansion, as in the magnetic case [19,20].…”

Section: A Comparison Of Real Partmentioning

confidence: 54%

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QED effective action in time dependent electric backgrounds

1998

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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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“…These results provide strong evidence that the expansion (33) of the exact result is an all-orders derivative expansion, as in the magnetic case [19,20].…”

Section: A Comparison Of Real Partmentioning

confidence: 54%

“…This resolvent approach has been applied successfully to spatially inhomogeneous magnetic backgrounds [19,20,18,12]. It has also been used previously by Chodos [8] in an analysis of the possibility of spontaneous chiral symmetry breaking for QED in time-varying background electric fields.…”

Section: Resolvent Methodsmentioning

confidence: 99%

QED effective action in time dependent electric backgrounds

1998

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“…Due to the similar functional form of Eqs. (38), (42) and (47) in comparison to Eqs. (36), the determination of the arbitrary functions on the hyper-surface T 0 is trivial:…”

Section: A Schwarzschild Solutionmentioning

confidence: 99%

The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory

2014

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A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge independent quantities. We shall see that in the QM-scheme we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz et al that deals with perturbation in the standard Einstein framework. For completeness, we compare the QMscheme to the gauge-independent method of Bardeen, a procedure consisting on particular choices of the perturbed variables as a combination of gauge dependent quantities.

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“…[28] It could be Borel summable however. [29] Conclusion: Supplementary works on this expansion would be welcome:…”

Section: Lowest Order Of the Derivative Expansionmentioning

confidence: 99%

Exact Renormalization Group Equations and the Field Theoretical Approach to Critical Phenomena

Bagnuls

Bervillier

2001

Int. J. Mod. Phys. A

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After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as the continuum limit and the renormalizability and the presence of singularities in the perturbative series are discussed.This paper has two parts. In the first part we restrict ourselves to the presentation of some selected issues taken from a recent review on the exact renormalization group (RG) equation (ERGE) in the pure scalar case.[1] In the second part we illustrate the Wilson continuum limit of field theory (or, equivalently, what may be understood as the nonperturbative renormalizability). More generally we would like to indicate how the historical first version of the RG, based on a perturbative approach, takes place in the more general nonperturbative framework developed by Wilson. The illustration will be done in the light of actual RG trajectories obtained from a numerical study of the ERGE in the local potential approximation. [2] 1 Selected issues What does "exact" mean ?The word "exact" means: a continuous (i.e. not discrete) realization of the Wilson RG transformation of the action in which no approximation is made and no expansion is involved with respect to some small parameter. We are here only interested in the differential form of the ERGE. One could think that the word exact is not adapted to the Wilson renormalization because, compared to the standard version of renormalization 1 , it involves a finite cutoff and it is only a semi-group. Nevertheless the historical first version is entirely contained in the Wilson theory (see part 2).

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An All-Orders Derivative Expansion

Cited by 14 publications

References 13 publications

QED effective action in time dependent electric backgrounds

QED effective action in time dependent electric backgrounds

The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory

Exact Renormalization Group Equations and the Field Theoretical Approach to Critical Phenomena

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