9 problems

The ${\cal B}_1$ basis diagonalizes curvature-related Wilson loop operators around edges, while the ${\cal B}_2$ basis encodes spatial geometric data such as areas and dihedral ang…

A four-dimensional Riemannian Spin Foam model with simplicity constraints is considered on triangulations related by Pachner moves, including the $5$--$1$ and $4$--$2$ moves. In th…

Barrett–Baez conjecture. Every 3-edge-connected $SL(2,\mathbb C)$ spin-network with invariants of this class is integrable; equivalently, the regularized evaluation of every such s…

Let $\Delta$ be a triangulated closed $3$-manifold, let $\Gamma$ be the $2$-skeleton of its dual cell complex, and let $N$ be the number of vertices of $\Delta$. Consider a sharp c…

Inverse-coupling conjecture. For $G=SU(2)$, the level is proportional to the inverse coupling,

Smolin's level–coupling conjecture. The value of $\lambda$ corresponding to $k$ is determined by

Smolin's conjecture. The parameters satisfy

Local-complexity conjecture. The class ${\cal S}$ also satisfies Restriction A2.

Triangulation-existence conjecture. Such a class of triangulations always exists for any 4-dimensional manifold, and can be given by the triangulations corresponding to the barycen…