5 problems

Let $E^c_{\kappa}$ and $e^c_{\kappa}$ be the energy levels defined above, and let ${\cal E}^c_{\kappa}$ be the Dirac–Fock energy on $G_N(P^+_{\kappa,\widetilde{W}} H^{1/2})$. A sub…

Weak Mittleman's conjecture. The Dirac–Fock model is an approximation of the electron-positron Hartree–Fock model in the precise sense of the displayed inequality. This weaker stat…

Let $e_q$ denote the physical ground state energy of the electron-positron Hartree–Fock model, obtained by maximizing the model's ground state energy over all allowed one-particle…

Let $e_{\rm Mitt}^{\nu,c,\tau}(N)$ denote the relativistic max-min energy and let $\Phi^{c,\tau,0}$ be a Dirac–Fock solution obtained in the $j=0$ case. Weaker Mittleman's conjectu…

Mittleman's conjecture. The max-min principle is attained by a solution of the Dirac–Fock system; more precisely, a solution is given by a pair