4 problems

Consider dilute one-dimensional spinless bosons and fermions, with energy expansions expressed in terms of their corresponding scattering lengths. Scattering-length universality co…

Barrier-removal conjecture. The barrier can be removed, so that Theorem holds in the larger Region $\mathrm{III}^{\prime}$.

The ground state energy and reduced density matrices admit a perturbative expansion whose first terms are denoted by $\gamma_0$ and $\gamma_1$. On the torus, translation invariance…

Triviality conjecture. For $d\geq 4$, the $\lambda\vert\boldsymbol{\phi}\vert^4$ theory of $\boldsymbol{\phi}$ is equivalent to a Gaussian (free) field theory.