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

Author:

Hidetoshi Taya, Charlie Ironside

Keyword:

High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Optics (physics.optics)

journal:

RIKEN-iTHEMS-Report-23

date:

2023-08-21 16:00:00

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.

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