QED Corrections in Unstable Vacuum

TL;DR

This paper investigates how quantum electrodynamics corrections affect vacuum stability in supercritical Coulomb fields, revealing enhanced spontaneous pair creation and nonperturbative effects near the supercritical threshold.

Contribution

It introduces the calculation of the imaginary part of QED corrections to explore vacuum instability and radiative pair creation in supercritical regimes, highlighting nonperturbative phenomena.

Findings

Radiative spontaneous pair creation is significantly enhanced near the supercritical threshold.

The total probability of pair creation may differ from Dirac theory predictions.

Nonperturbative effects become prominent in the supercritical Coulomb field regime.

Abstract

Self-energy and vacuum polarization effects in quantum electrodynamics (QED) are calculated for the supercritical Coulomb field, where Dirac energy levels become embedded in the negative-energy continuum. In this regime, the quantum vacuum becomes unstable, resulting in spontaneous electron-positron pair creation. By calculating the imaginary part of the QED correction, we gain access to an unexplored channel of vacuum instability: radiative spontaneous pair creation. Our results show that this radiative channel is greatly enhanced in the vicinity of the threshold of the supercritical regime, providing evidence for nonperturbative effects with respect to the fine-structure constant $\alpha$. We therefore conjecture that the total probability of spontaneous pair creation could differ significantly from the predictions of Dirac theory, especially near the supercritical threshold.