TY  - JOUR
AU  - Borja, E. F.
AU  - Diaz-Polo, J.
AU  - Garay, I.
AU  - Livine, E. R.
PY  - 2010
DA  - 2010//
TI  - Dynamics for a 2-vertex quantum gravity model
T2  - Class. Quantum Gravity
JO  - Classical and Quantum Gravity
SP  - 235010
EP  - 34pp
VL  - 27
IS  - 23
PB  - Iop Publishing Ltd
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.
SN  - 0264-9381
UR  - http://arxiv.org/abs/1006.2451
UR  - https://doi.org/10.1088/0264-9381/27/23/235010
DO  - 10.1088/0264-9381/27/23/235010
LA  - English
N1  - ISI:000284211600011
ID  - Borja_etal2010
ER  -