8 problems

The radial Dirac equation is the two-component system for radial functions $f(r)$ and $g(r)$ with energy $E$, mass $M$, centrifugal term $U(r)=\kappa/r$, electrostatic potential…

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…

Monotonicity conjecture.

General-charge conjecture.

Let $\boldsymbol{A}_{\rm ext}=(0,0)$ be the vanishing external four-potential, and let $\boldsymbol{A}=(V,A)$ range over the divergence-free homogeneous Sobolev space in the min-ma…

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