Vacuum photon emission and mean electromagnetic field in pair-creating external backgrounds

• URL: http://arxiv.org/abs/2606.12547v1
• Date: Wed, 10 Jun 2026 18:01:00 GMT
• Title: Vacuum photon emission and mean electromagnetic field in pair-creating external backgrounds
• Abstract summary: We develop a perturbative description of vacuum radiative processes in quantum electrodynamics.<n>We derive the mean number density of emitted photons through the second nonvanishing order in the fine-structure constant.<n>We compute the mean electromagnetic field through order $e3$, including the electromagnetic dressing of the induced vacuum current.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a perturbative description of vacuum radiative processes in quantum electrodynamics with a prescribed external electromagnetic background capable of producing electron-positron pairs. Since the initial vacuum is then unstable and the in- and out-vacua are inequivalent, radiative observables require a real-time formulation beyond the ordinary in-out approach of vacuum-stable QED. Using the Keldysh-Schwinger-Fradkin nonequilibrium technique, we derive the mean number density of emitted photons through the second nonvanishing order in the fine-structure constant. The leading term, of order $α$, reproduces the known vertex and tadpole mechanisms, while the complete order-$α^2$ correction contains interference, loop, and induced-current contributions. We also give an independent derivation based on the spectral decomposition of the identity operator in the in-Fock space, where the photon number density is represented as a sum of squared transition amplitudes and vacuum-disconnected terms are canceled by the optical theorem generalized to an unstable vacuum. In addition, we compute the mean electromagnetic field through order $e^3$, including the electromagnetic dressing of the induced vacuum current, and verify it using the corresponding Schwinger-Dyson equations. The final formulas are expressed in terms of exact solutions and propagators of the Dirac equation in the external background and apply to general spacetime-dependent field configurations.

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