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On the Hartree-Fock Equations of the Electron-Positron Field

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We study the energy of relativistic electrons and positrons interacting via the second quantized Coulomb potential in the field of a nucleus of charge Z within the Hartree-Fock approximation. We show that the associated functional has a minimizer. In addition, all minimizers are purely electronic states, they are projections, and fulfill the no-pair Dirac-Fock equations.

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Authors and Affiliations

  1. Département de Mathématiques, Université du Sud Toulon-Var, Avenue de l’Université, BP 132, 83957, La Garde Cedex, France

    Jean-Marie Barbaroux

  2. Swiss Banking Institute, Universität Zürich, Plattenstr. 14, 8032, Zürich, Switzerland

    Walter Farkas

  3. Département de Mathématiques, Université Paris Sud, Bâtiment 425, 91405, Orsay Cédex, France

    Bernard Helffer

  4. Mathematisches Institut, LMU, Theresienstr. 39, 80333, München, Germany

    Heinz Siedentop

Authors
  1. Jean-Marie Barbaroux
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  2. Walter Farkas
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  3. Bernard Helffer
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  4. Heinz Siedentop
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Corresponding author

Correspondence to Heinz Siedentop.

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Communicated by B. Simon

2003 The authors. Reproduction of this article for non-commercial purposes by any means is permitted.

Acknowledgement We thank K. Yajima and M. Huber for critical reading of a preliminary version of the manuscript and D. Hundertmark for useful and enjoyable discussions concerning various aspects of this paper. One of us, JMB, thanks B. Grébert for useful discussions concerning Sect. 3. Financial support of the Ministère de l’Education Nationale, de la Recherche et de la Technologie through ACI Blanche, of the Bayerisch-Französisches Hochschulzentrum, of the European Union through the IHP network “Analysis and Quantum”, contract HPRN-CT-2002-00277, are gratefully acknowledged. Part of the work was done while three of us, JMB, BH, and HS, were visiting the Mittag-Leffler Institute; its support is also gratefully acknowledged.

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Barbaroux, JM., Farkas, W., Helffer, B. et al. On the Hartree-Fock Equations of the Electron-Positron Field. Commun. Math. Phys. 255, 131–159 (2005). https://doi.org/10.1007/s00220-004-1156-x

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  • DOI: https://doi.org/10.1007/s00220-004-1156-x

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