Dynamics for a 2-vertex Quantum Gravity Model

Details Dynamics for a 2-vertex Quantum Gravity Model Dynamics for a 2-vertex Quantum Gravity Model

2010-06-12

arxiv.org/abs/1006.2451v2

Class.Quant.Grav.27:235010,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28 pages, v2: typos corrected

Scientific paper

10.1088/0264-9381/27/23/235010

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.

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