14 problems

Lewandowski–Thiemann conjecture. It should always be possible to find degenerate segments $s_l$ such that the portion of the web between every two subsequent intervals corresponds…

Let $\gamma$ be a loop and let $\operatorname{Jones}_\Lambda(\gamma)$ denote the Jones Polynomial appearing in the expansion of the Kauffman Bracket with cosmological constant…

Smolin's hypothesis. This finite-dimensional Chern–Simons state space is the space of all physical states of quantum gravity on $S$ that satisfy the self-dual boundary conditions a…

Let $[... ]$ be the dense domain of finite-particle states generated by Schwartz test functions, contained in the Hilbert space $[... ]$. For a distribution $F[... ]$ such that…

Smolin's conjecture. CFT degrees of freedom should appear around loop punctures.

The setting is that of polyhedra in constant-curvature three-dimensional model spaces, with tetrahedral faces flatly embedded in the three-sphere $\mathrm{S}^3$ or hyperbolic three…

Let $\Lambda$ be the cosmological constant, and let the local gauge symmetry be described by the Lorentz group or by the local $\mathrm{SU}(2)$ gauge group. Quantum-deformation con…

A q-deformed gauge group is expected to describe loop-gravity geometries with nonzero cosmological constant. In the undeformed theory, the gauge group is $\mathrm{SU}(2)$ and closu…

Let $D$ be odd or even, and let $\widetilde{\mathfrak{C}}_{D,coloured}$ be the set of labelled loopless $D$-regular boundary graphs whose edges can be coloured with $D$ colours so…

The entropy step constant is defined by … Here $\Delta a$ is the characteristic width of the entropy steps, while the subscripts DL, GM, and ENP denote the different loop-quantum-g…

Holonomy operator ordering conjecture. The holonomy operator around $\mathcal L$ acts on spin-network states as

U(N) spinor representation conjecture. The space of such functions is isomorphic to

Functional-space conjecture. The resulting Hilbert space should admit a better characterization as such a functional space of generalized flux fields.

In loop quantum gravity, the black-hole entropy spectrum exhibits a quantization phenomenon, characterized by a preferred spacing in the entropy or area spectrum. Macroscopic-black…