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Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field. (English) Zbl 0913.35113
Summary: We investigate stability of matter of the Hartree-Fock functional of the relativistic electron-positron field – in suitable second quantization – interacting via a second quantized Coulomb field and a classical magnetic field. We are able to show that stability holds for a range of nuclear charges \(Z_1,\dots, Z_K\leq Z\) and fine structure constants \(\alpha\) that include the physical value of \(\alpha\) and elements up to holmium \((Z= 67)\).

MSC:
35Q40 PDEs in connection with quantum mechanics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81V10 Electromagnetic interaction; quantum electrodynamics
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