5 research outputs found
Physical boundary state for the quantum tetrahedron
We consider stability under evolution as a criterion to select a physical
boundary state for the spinfoam formalism. As an example, we apply it to the
simplest spinfoam defined by a single quantum tetrahedron and solve the
associated eigenvalue problem at leading order in the large spin limit. We show
that this fixes uniquely the free parameters entering the boundary state.
Remarkably, the state obtained this way gives a correlation between edges which
runs at leading order with the inverse distance between the edges, in agreement
with the linearized continuum theory. Finally, we give an argument why this
correlator represents the propagation of a pure gauge, consistently with the
absence of physical degrees of freedom in 3d general relativity.Comment: 20 pages, 6 figure
Numerical indications on the semiclassical limit of the flipped vertex
We introduce a technique for testing the semiclassical limit of a quantum
gravity vertex amplitude. The technique is based on the propagation of a
semiclassical wave packet. We apply this technique to the newly introduced
"flipped" vertex in loop quantum gravity, in order to test the intertwiner
dependence of the vertex. Under some drastic simplifications, we find very
preliminary, but surprisingly good numerical evidence for the correct classical
limit.Comment: 4 pages, 8 figure
Area-angle variables for general relativity
We introduce a modified Regge calculus for general relativity on a
triangulated four dimensional Riemannian manifold where the fundamental
variables are areas and a certain class of angles. These variables satisfy
constraints which are local in the triangulation. We expect the formulation to
have applications to classical discrete gravity and non-perturbative approaches
to quantum gravity.Comment: 7 pages, 1 figure. v2 small changes to match published versio
Graviton propagator in loop quantum gravity
We compute some components of the graviton propagator in loop quantum
gravity, using the spinfoam formalism, up to some second order terms in the
expansion parameter.Comment: 41 pages, 6 figure