Static Electron–Positron Pair Creation in Strong Fields for a Non-linear Dirac Model

被引:0
|
作者
Julien Sabin
机构
[1] Université de Cergy-Pontoise,Département de Mathématiques, CNRS UMR 8088
来源
Annales Henri Poincaré | 2013年 / 14卷
关键词
Quantum Electrodynamic; Static Pair; Exchange Term; Pair Creation; Pairing Matrix;
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摘要
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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1-\exp(-\kappa Z^{2/3})}$$\end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Z \to+\infty}$$\end{document} which gives the expected bounds.
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页码:1349 / 1382
页数:33
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