860 research outputs found
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
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.
A Lorentzian Gromov-Hausdoff notion of distance
This paper is the first of three in which I study the moduli space of
isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I
introduce a notion of Gromov-Hausdorff distance which makes this moduli space
into a metric space. Further properties of this metric space are studied in the
next papers. The importance of the work can be situated in fields such as
cosmology, quantum gravity and - for the mathematicians - global Lorentzian
geometry.Comment: 20 pages, 0 figures, submitted to Classical and quantum gravity,
seriously improved presentatio
Gravity and Matter in Causal Set Theory
The goal of this paper is to propose an approach to the formulation of
dynamics for causal sets and coupled matter fields. We start from the continuum
version of the action for a Klein-Gordon field coupled to gravity, and rewrite
it first using quantities that have a direct correspondent in the case of a
causal set, namely volumes, causal relations, and timelike lengths, as
variables to describe the geometry. In this step, the local Lagrangian density
for a set of fields is recast into a quasilocal expression
that depends on pairs of causally related points and
is a function of the values of in the Alexandrov set defined by those
points, and whose limit as and approach a common point is .
We then describe how to discretize , and use it to define a
discrete action.Comment: 13 pages, no figures; In version 2, friendlier results than in
version 1 are obtained following much shorter derivation
Symmetries, Horizons, and Black Hole Entropy
Black holes behave as thermodynamic systems, and a central task of any
quantum theory of gravity is to explain these thermal properties. A statistical
mechanical description of black hole entropy once seemed remote, but today we
suffer an embarrassment of riches: despite counting very different states, many
inequivalent approaches to quantum gravity obtain identical results. Such
``universality'' may reflect an underlying two-dimensional conformal symmetry
near the horizon, which can be powerful enough to control the thermal
characteristics independent of other details of the theory. This picture
suggests an elegant description of the relevant degrees of freedom as
Goldstone-boson-like excitations arising from symmetry breaking by the
conformal anomaly.Comment: 6 pages; first prize essay, 2007 Gravity Research Foundation essay
contes
Short-distance regularity of Green's function and UV divergences in entanglement entropy
Reformulating our recent result (arXiv:1007.1246 [hep-th]) in coordinate
space we point out that no matter how regular is short-distance behavior of
Green's function the entanglement entropy in the corresponding quantum field
theory is always UV divergent. In particular, we discuss a recent example by
Padmanabhan (arXiv:1007.5066 [gr-qc]) of a regular Green's function and show
that provided this function arises in a field theory the entanglement entropy
in this theory is UV divergent and calculate the leading divergent term.Comment: LaTeX, 6 page
Thermodynamics and area in Minkowski space: Heat capacity of entanglement
Tracing over the degrees of freedom inside (or outside) a sub-volume V of
Minkowski space in a given quantum state |psi>, results in a statistical
ensemble described by a density matrix rho. This enables one to relate quantum
fluctuations in V when in the state |psi>, to statistical fluctuations in the
ensemble described by rho. These fluctuations scale linearly with the surface
area of V. If V is half of space, then rho is the density matrix of a canonical
ensemble in Rindler space. This enables us to `derive' area scaling of
thermodynamic quantities in Rindler space from area scaling of quantum
fluctuations in half of Minkowski space. When considering shapes other than
half of Minkowski space, even though area scaling persists, rho does not have
an interpretation as a density matrix of a canonical ensemble in a curved, or
geometrically non-trivial, background.Comment: 17 page
Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle
Causal fermion systems are introduced as a general mathematical framework for
formulating relativistic quantum theory. By specializing, we recover earlier
notions like fermion systems in discrete space-time, the fermionic projector
and causal variational principles. We review how an effect of spontaneous
structure formation gives rise to a topology and a causal structure in
space-time. Moreover, we outline how to construct a spin connection and
curvature, leading to a proposal for a "quantum geometry" in the Lorentzian
setting. We review recent numerical and analytical results on the support of
minimizers of causal variational principles which reveal a "quantization
effect" resulting in a discreteness of space-time. A brief survey is given on
the correspondence to quantum field theory and gauge theories.Comment: 23 pages, LaTeX, 2 figures, footnote added on page
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