1,072 research outputs found
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
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
The Semiclassical Limit of Loop Quantum Cosmology
The continuum and semiclassical limits of isotropic, spatially flat loop
quantum cosmology are discussed, with an emphasis on the role played by the
Barbero-Immirzi parameter \gamma in controlling space-time discreteness. In
this way, standard quantum cosmology is shown to be the simultaneous limit
\gamma \to 0, j \to \infty of loop quantum cosmology. Here, j is a label of the
volume eigenvalues, and the simultaneous limit is technically the same as the
classical limit \hbar \to 0, l \to \infty of angular momentum in quantum
mechanics. Possible lessons for semiclassical states at the dynamical level in
the full theory of quantum geometry are mentioned.Comment: 10 page
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
Where are the degrees of freedom responsible for black hole entropy?
Considering the entanglement between quantum field degrees of freedom inside
and outside the horizon as a plausible source of black hole entropy, we address
the question: {\it where are the degrees of freedom that give rise to this
entropy located?} When the field is in ground state, the black hole area law is
obeyed and the degrees of freedom near the horizon contribute most to the
entropy. However, for excited state, or a superposition of ground state and
excited state, power-law corrections to the area law are obtained, and more
significant contributions from the degrees of freedom far from the horizon are
shown.Comment: 6 pages, 4 figures, Invited talk at Theory Canada III, Edmonton,
Alberta, Canada, June 16, 200
Thermal behavior induced by vacuum polarization on causal horizons in comparison with the standard heat bath formalism
Modular theory of operator algebras and the associated KMS property are used
to obtain a unified description for the thermal aspects of the standard heat
bath situation and those caused by quantum vacuum fluctuations from
localization. An algebraic variant of lightfront holography reveals that the
vacuum polarization on wedge horizons is compressed into the lightray
direction. Their absence in the transverse direction is the prerequisite to an
area (generalized Bekenstein-) behavior of entropy-like measures which reveal
the loss of purity of the vacuum due to restrictions to wedges and their
horizons. Besides the well-known fact that localization-induced (generalized
Hawking-) temperature is fixed by the geometric aspects, this area behavior
(versus the standard volume dependence) constitutes the main difference between
localization-caused and standard thermal behavior.Comment: 15 page Latex, dedicated to A. A. Belavin on the occasion of his 60th
birthda
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
On alternative approaches to Lorentz violation in loop quantum gravity inspired models
Recent claims point out that possible violations of Lorentz symmetry
appearing in some semiclassical models of extended matter dynamics motivated by
loop quantum gravity can be removed by a different choice of canonically
conjugated variables. In this note we show that such alternative is
inconsistent with the choice of variables in the underlying quantum theory
together with the semiclassical approximation, as long as the correspondence
principle is maintained. A consistent choice will violate standard Lorentz
invariance. Thus, to preserve a relativity principle in this framework, the
linear realization of Lorentz symmetry should be extended or superseded.Comment: 4 pages, revtex4, no figures, references adde
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