7 problems

Extension conjecture. The same bound should hold for every $s\geq1$: there should exist a finite $c(s)$, with $c(s)\to\infty$ as $s\to\infty$, such that

Let $s>0$, $d\geq 1$, and $\lambda>0$. For the Lieb–Thirring inequality with kinetic energy $(-\Delta)^s$ and repulsive interaction $\lambda\lvert x_i-x_j\rvert^{-2s}$, let…

Binding conjecture. For every $N\geq2$ and every $1<p<\min\left(2,1+\frac{2}{d}\right)$, the binding inequalities

BBGKY–GP hierarchy conjecture. The BBGKY and GP hierarchies should provide the required link for deriving the geometry associated with the Hamiltonian formulation of the nonlinear…

Let ${\mathcal F}$ be the bosonic Fock space, let ${\mathcal H}$ be the many-body Hamiltonian, and let ${\mathcal A}(\phi)$ and ${\mathcal B}(k)$ denote the coherent-state and pair…

Fractional Lieb-Thirring coupling conjecture. The optimal constant also satisfies

Let the interaction parameter satisfy $\beta\in(0,1]$, and let $\{\Gamma_N\}_{N=1}^{\infty}$ be a sequence of quantum BBGKY hierarchy solutions satisfying the energy condition … fo…