3 research outputs found
Entropy in the Classical and Quantum Polymer Black Hole Models
We investigate the entropy counting for black hole horizons in loop quantum
gravity (LQG). We argue that the space of 3d closed polyhedra is the classical
counterpart of the space of SU(2) intertwiners at the quantum level. Then
computing the entropy for the boundary horizon amounts to calculating the
density of polyhedra or the number of intertwiners at fixed total area.
Following the previous work arXiv:1011.5628, we dub these the classical and
quantum polymer models for isolated horizons in LQG. We provide exact
micro-canonical calculations for both models and we show that the classical
counting of polyhedra accounts for most of the features of the intertwiner
counting (leading order entropy and log-correction), thus providing us with a
simpler model to further investigate correlations and dynamics. To illustrate
this, we also produce an exact formula for the dimension of the intertwiner
space as a density of "almost-closed polyhedra".Comment: 24 page
Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
Loop Quantum Gravity defines the quantum states of space geometry as spin
networks and describes their evolution in time. We reformulate spin networks in
terms of harmonic oscillators and show how the holographic degrees of freedom
of the theory are described as matrix models. This allow us to make a link with
non-commutative geometry and to look at the issue of the semi-classical limit
of LQG from a new perspective. This work is thought as part of a bigger project
of describing quantum geometry in quantum information terms.Comment: 16 pages, revtex, 3 figure