 0831 Christian HAINZL, Mathieu LEWIN and Eric SERE
 Existence of Atoms and Molecules in the MeanField Approximation of NoPhoton Quantum Electrodynamics
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Feb 19, 08

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Abstract. The BogoliubovDiracFock (BDF) model is the meanfield approximation of nophoton Quantum Electrodynamics.
The present paper is devoted to the study of the minimization of the BDF energy functional \emph{under a charge constraint}. An associated minimizer, if it exists, will usually represent the ground state of a system of $N$ electrons interacting with the Dirac sea, in an external electrostatic field generated by one or several fixed nuclei. We prove that such a minimizer exists when a binding (HVZtype) condition holds. We also derive, study and interpret the equation satisfied by such a minimizer.
Finally, we provide two regimes in which the binding condition is fulfilled, obtaining the existence of a minimizer in these cases. The first is the weak coupling regime for which the coupling constant $\alpha$ is small whereas $\alpha Z$ and the particle number $N$ are fixed. The second is the nonrelativistic regime in which the speed of light tends to infinity (or equivalently $\alpha$ tends to zero) and $Z$, $N$ are fixed. We also prove that the electronic solution converges in the nonrelativistic limit towards a HartreeFock ground state.
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