33 citations · 75 across the 7 of their papers we have counts for
7 papers
Abelian 2+1D Loop Quantum Gravity Coupled to a Scalar Field
Christoph Charles
In order to study 3d loop quantum gravity coupled to matter, we consider a simplified model of abelian quantum gravity, the so-called U(1)^3 model. Abelian gravity coupled to a sca…
Simplicity constraints: a 3d toy-model for Loop Quantum Gravity
Christoph Charles
In Loop Quantum Gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge-fixing of the theory, correspond to a parametri…
Renormalization and Coarse-graining of Loop Quantum Gravity
Christoph Charles
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-…
The closure constraint for the hyperbolic tetrahedron as a Bianchi identity
Christoph Charles, Etera R. Livine
The closure constraint is a central piece of the mathematics of loop quantum gravity. It encodes the gauge invariance of the spin network states of quantum geometry and provides th…
The Fock Space of Loopy Spin Networks for Quantum Gravity
Christoph Charles, Etera R. Livine
In the context of the coarse-graining of loop quantum gravity, we introduce loopy and tagged spin networks, which generalize the standard spin network states to account explicitly…
Ashtekar-Barbero holonomy on the hyperboloid: Immirzi parameter as a Cut-off for Quantum Gravity
Christoph Charles, Etera R. Livine
In the context of the geometrical interpretation of the spin network states of Loop Quantum Gravity, we look at the holonomies of the Ashtekar-Barbero connection on loops embedded…
Closure constraints for hyperbolic tetrahedra
Christoph Charles, Etera R. Livine
We investigate the generalization of loop gravity's twisted geometries to a q-deformed gauge group. In the standard undeformed case, loop gravity is a formulation of general relati…