Static Electron-Positron Pair Creation in Strong Fields for a Nonlinear Dirac model

TL;DR

This paper analyzes the probability of static electron-positron pair creation in a strong external field within a simplified quantum electrodynamics model, revealing an exponential behavior as the field strength increases.

Contribution

It provides a rigorous proof of the asymptotic behavior of pair creation probability in the Hartree-Fock approximation for large external fields.

Findings

Probability of pair creation behaves as 1 - exp(-κ Z^{2/3}) for large Z.

Estimates vacuum expectation of quasi-free states in terms of particle number.

Asymptotic analysis of Hartree-Fock energy as Z approaches infinity.

Abstract

We consider the Hartree-Fock approximation of Quantum Electrodynamics, with the exchange term neglected. We prove that the probability of static electron-positron pair creation for the Dirac vacuum polarized by an external field of strength $Z$ behaves as $1-\exp(-\kappa Z^{2/3})$ for $Z$ large enough. Our method involves two steps. First we estimate the vacuum expectation of general quasi-free states in terms of their total number of particles, which can be of general interest. Then we study the asymptotics of the Hartree-Fock energy when $Z\to+\infty$ which gives the expected bounds.