Remarks on the Mittleman max?min variational method for the electron-positron field

Barbaroux, Esteban and Sere have investigated the relation between Mittleman's max–min principle and the solutions of the Dirac–Fock equations. Their comparison is valid in the non-relativistic limit, but it does not contain quantitative estimates. We generalize their result of non-agreement in the case of one electron and show that this non-agreement holds for the physical value of the fine structure constant if Z < 42 (molybdenum).

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