Kramers-Kr\"onig approach to the electric permittivity of the vacuum in a strong constant electric field

TL;DR

This paper investigates how a strong electric field alters the vacuum's electric permittivity in QED, revealing oscillatory behavior and linking it to pair production, using a novel theoretical approach that does not assume weak fields.

Contribution

The authors develop a non-equilibrium linear-response theory combined with the Kramers-Kr"onig relation to analyze vacuum permittivity under strong fields without weak-field assumptions.

Findings

Electric permittivity shows oscillations with probe frequency.

Vacuum permittivity correlates with electron-positron pair production.

Method applies beyond weak-field and low-frequency limits.

Abstract

We study the electric permittivity of the QED vacuum in the presence of a strong constant electric field, motivated by the analogy between the dynamically-assisted Schwinger effect in strong-field QED and the Franz-Keldysh effect in semiconductor physics. We develop a linear-response theory based on the non-equilibrium in-in formalism and the Furry-picture perturbation theory, with which and also utilizing the Kramers-Kr\"onig relation, we calculate the electric permittivity without assuming weak fields and low-frequency probes. We discover that the electric permittivity exhibits characteristic oscillating dependence on the probe frequency, which directly reflects the change of the QED-vacuum structure by the strong field. We also establish a quantitative correspondence between the electric permittivity and the number of electron-positron pairs produced by the dynamically-assisted Schwinger effect.