Kramers-Krönig approach to the electric permittivity of the vacuum in a strong constant electric field
arXiv:2308.11248 · doi:10.1103/PhysRevD.108.096005
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-Krönig 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.
arXiv comment27 pages, 6 figures; v2: references added, discussions improved, to appear in Phys. Rev. D
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