Stability of the Relativistic Electron-Positron Field of Atoms in Hartree-Fock Approximation: Heavy Elements

We show that the modulus of the Coulomb Dirac operator with a sufficiently small coupling constant bounds the modulus of the free Dirac operator from above up to a multiplicative constant depending on the product of the nuclear charge and the electronic charge. This bound sharpens a result of Bach et al \cite{Bachetal1999} and allows to prove the positivity of the relativistic electron-positron field of an atom in Hartree-Fock approximation for all elements occurring in nature.

2000 Mathematics Subject Classification: 35Q40, 81Q10

Keywords and Phrases: Dirac operator, stability of matter, QED, generalized Hartree-Fock states

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