PT Journal
AU Borja, EF
   Diaz-Polo, J
   Garay, I
   Livine, ER
TI Dynamics for a 2-vertex quantum gravity model
SO Classical and Quantum Gravity
JI Class. Quantum Gravity
PY 2010
BP 235010
EP 34pp
VL 27
IS 23
DI 10.1088/0264-9381/27/23/235010
LA English
AB We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N)-invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.
ER