2,250 research outputs found

### Statistical geometry of random weave states

I describe the first steps in the construction of semiclassical states for
non-perturbative canonical quantum gravity using ideas from classical,
Riemannian statistical geometry and results from quantum geometry of spin
network states. In particular, I concentrate on how those techniques are
applied to the construction of random spin networks, and the calculation of
their contribution to areas and volumes.Comment: 10 pages, LaTeX, submitted to the Proceedings of the IX Marcel
Grossmann Meeting, Rome, July 2-8, 200

### Manifold dimension of a causal set: Tests in conformally flat spacetimes

This paper describes an approach that uses flat-spacetime dimension
estimators to estimate the manifold dimension of causal sets that can be
faithfully embedded into curved spacetimes. The approach is invariant under
coarse graining and can be implemented independently of any specific curved
spacetime. Results are given based on causal sets generated by random
sprinklings into conformally flat spacetimes in 2, 3, and 4 dimensions, as well
as one generated by a percolation dynamics.Comment: 8 pages, 8 figure

### A combinatorial approach to discrete geometry

We present a paralell approach to discrete geometry: the first one introduces
Voronoi cell complexes from statistical tessellations in order to know the mean
scalar curvature in term of the mean number of edges of a cell. The second one
gives the restriction of a graph from a regular tessellation in order to
calculate the curvature from pure combinatorial properties of the graph.
Our proposal is based in some epistemological pressupositions: the
macroscopic continuous geometry is only a fiction, very usefull for describing
phenomena at certain sacales, but it is only an approximation to the true
geometry. In the discrete geometry one starts from a set of elements and the
relation among them without presuposing space and time as a background.Comment: LaTeX, 5 pages with 3 figures. To appear in the Proceedings of the
XXVIII Spanish Relativity Meeting (ERE2005), 6-10 September 2005, Oviedo,
Spai

### Models for Discrete Quantum Gravity

We first discuss a framework for discrete quantum processes (DQP). It is
shown that the set of q-probability operators is convex and its set of extreme
elements is found. The property of consistency for a DQP is studied and the
quadratic algebra of suitable sets is introduced. A classical sequential growth
process is "quantized" to obtain a model for discrete quantum gravity called a
quantum sequential growth process (QSGP). Two methods for constructing concrete
examples of QSGP are provided.Comment: 15 pages which include 2 figures which were created using LaTeX and
contained in the fil

### Semiclassical States for Constrained Systems

The notion of semi-classical states is first sharpened by clarifying two
issues that appear to have been overlooked in the literature. Systems with
linear and quadratic constraints are then considered and the group averaging
procedure is applied to kinematical coherent states to obtain physical
semi-classical states. In the specific examples considered, the technique turns
out to be surprisingly efficient, suggesting that it may well be possible to
use kinematical structures to analyze the semi-classical behavior of physical
states of an interesting class of constrained systems.Comment: 27 pages, 3 figures. V2 discussion expanded. Final version to be
published in PR

### Angular quantization and the density matrix renormalization group

Path integral techniques for the density matrix of a one-dimensional
statistical system near a boundary previously employed in black-hole physics
are applied to providing a new interpretation of the density matrix
renormalization group: its efficacy is due to the concentration of quantum
states near the boundary.Comment: 8 pages, 3 figures, to appear in Mod. Phys. Lett.

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