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## On Locality in Quantum General Relativity and Quantum Gravity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/03/1996
Português

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The physical concept of locality is first analyzed in the special
relativistic quantum regime, and compared with that of microcausality and the
local commutativity of quantum fields. Its extrapolation to quantum general
relativity on quantum bundles over curved spacetime is then described. It is
shown that the resulting formulation of quantum-geometric locality based on the
concept of local quantum frame incorporating a fundamental length embodies the
key geometric and topological aspects of this concept. Taken in conjunction
with the strong equivalence principle and the path-integral formulation of
quantum propagation, quantum-geometric locality leads in a natural manner to
the formulation of quantum-geometric propagation in curved spacetime. Its
extrapolation to geometric quantum gravity formulated over quantum spacetime is
described and analyzed.; Comment: Mac-Word file translated to postscript for submission. The author may
be reached at: e.prugovecki@utoronto.ca To appear in Found. Phys. vol. 27,
1997

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## A Mathematicians' View of Geometrical Unification of General Relativity and Quantum Physics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/12/2015
Português

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This document contains a description of physics entirely based on a geometric
presentation: all of the theory is described giving only a pseudo-riemannian
manifold (M, g) of dimension n > 5 for which the g tensor is, in studied
domains, almost everywhere of signature (-, -, +, ..., +). No object is added
to this space-time, no general principle is supposed. The properties we impose
to some domains of (M, g) are only simple geometric constraints, essentially
based on the concept of "curvature". These geometric properties allow to
define, depending on considered cases, some objects (frequently depicted by
tensors) that are similar to the classical physics ones, they are however built
here only from the g tensor. The links between these objects, coming from their
natural definitions, give, applying standard theorems from the
pseudo-riemannian geometry, all equations governing physical phenomena usually
described by classical theories, including general relativity and quantum
physics. The purely geometric approach introduced hear on quantum phenomena is
profoundly different from the standard one. Neither Lagrangian nor Hamiltonian
are used. This document ends with a quick presentation of our approach of
complex quantum phenomena usually studied by quantum field theory.

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## Structure, Individuality and Quantum Gravity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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After reviewing various interpretations of structural realism, I adopt here a
definition that allows both relations between things that are already
individuated (which I call ``relations between things'') and relations that
individuate previously un-individuated entities ("things between relations").
Since both space-time points in general relativity and elementary particles in
quantum theory fall into the latter category, I propose a principle of maximal
permutability as a criterion for the fundamental entities of any future theory
of ``quantum gravity''; i.e., a theory yielding both general relativity and
quantum field theory in appropriate limits. Then I review of a number of
current candidates for such a theory. First I look at the effective field
theory and asymptotic quantization approaches to general relativity, and then
at string theory. Then a discussion of some issues common to all approaches to
quantum gravity based on the full general theory of relativity argues that
processes, rather than states should be taken as fundamental in any such
theory. A brief discussion of the canonical approach is followed by a survey of
causal set theory, and a new approach to the question of which space-time
structures should be quantized ends the paper.; Comment: 39 pages...

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## Noncommutative Unification of General Relativity and Quantum Mechanics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/04/2005
Português

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In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have
proposed a model unifying general relativity and quantum mechanics based on a
noncommutative geometry. This geometry was developed in terms of a
noncommutative algebra A defined on a transformation groupoid given by the
action of a group G on a space E. Owing to the fact that G was assumed to be
finite it was possible to compute the model in full details. In the present
paper we develop the model in the case when G is a noncompact group. It turns
out that also in this case the model works well. The case is important since to
obtain physical effects predicted by the model we should assume that G is a
Lorentz group or some of its representations. We show that the generalized
Einstein equation of the model has the form of the eigenvalue equation for the
generalized Ricci operator, and all relevant operators in the quantum sector of
the model are random operators; we study their dynamics. We also show that the
model correctly reproduces general relativity and the usual quantum mechanics.
It is interesting that the latter is recovered by performing the measurement of
any observable. In the act of such a measurement the model ``collapses'' to the
usual quantum mechanics.; Comment: 23 LaTex pages

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## The Chrono'Geometrical Structure of Special and General Relativity: Towards a Background-Independent Description of the Gravitational Field and Elementary Particles

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/04/2004
Português

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Since the main open problem of contemporary physics is to find a unified
description of the four interactions, we present a possible scenario which,
till now only at the classical level, is able to englobe experiments ranging
from experimental space gravitation to atomic and particle physics. After a
reformulation of special relativistic physics in a form taking into account the
non-dynamical chrono-geometrical structure of Minkowski space-time
(parametrized Minkowski theories and rest-frame instant form) and in particular
the conventionality of simultaneity (re-phrased as a gauge freedom), a model of
canonical metric and tetrad gravity is proposed in a class of space-times where
the deparametrization to Minkowski space-time is possible. In them it is
possible to give a post-Minkowskian background-independent description of the
gravitational field and of matter. The study of the dynamical
chrono-geometrical structure of these space-times allows to face
interpretational problems like the physical identification of point-events (the
Hole Argument), the distinction between inertial (gauge) and tidal (Dirac
observables) effects, the dynamical nature of simultaneity in general
relativity and to find background-independent gravitational waves. These
developments are possible at the Hamiltonian level due to a systematic use of
Dirac-Bergmann theory of constraints. Finally there is a proposal for a new
coordinate- and background-independent quantization scheme for gravity.; Comment: 71 pages...

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## Kinematic self-similar solutions in general relativity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/05/2004
Português

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The gravitational interaction is scale-free in both Newtonian gravity and
general theory of relativity. The concept of self-similarity arises from this
nature. Self-similar solutions reproduce themselves as the scale changes. This
property results in great simplification of the governing partial differential
equations. In addition, some self-similar solutions can describe the asymptotic
behaviors of more general solutions. Newtonian gravity contains only one
dimensional constant, the gravitational constant, while the general relativity
contains another dimensional constant, the speed of light, besides the
gravitational constant. Due to this crucial difference, incomplete similarity
can be more interesting in general relativity than in Newtonian gravity.
Kinematic self-similarity has been defined and studied as an example of
incomplete similarity in general relativity, in an effort to pursue a wider
application of self-similarity in general relativity. We review the
mathematical and physical aspects of kinematic self-similar solutions in
general relativity.; Comment: 29 pages, no figures, 1 table. This is a review for a part of the
book "Progress in General Relativity and Quantum Cosmology Research" (Nova
Science Publ.,2004)

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## The Dynamic Space of General Relativity in Second Atomization

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The notion that the geometry of our space-time is not only a static
background but can be physically dynamic is well established in general
relativity. Geometry can be described as shaped by the presence of matter,
where such shaping manifests itself as gravitational force. We consider here
probabilistic or atomistic models of such space-time, in which the active
geometry emerges from a statistical distribution of 'atoms'. Such atoms are not
to be confused with their chemical counterparts, however the shift of
perspective obtained in analyzing a gas via its molecules rather than its bulk
properties is analogous to this "second atomization". In this atomization,
space-time itself (i.e. the meter and the second) is effectively atomized, so
the atoms themselves must exist in a 'subspace'.
Here we build a simple model of such a space-time from the ground up,
establishing a route for more complete theories, and enabling a review of
recent work. We first introduce the motivation behind statistical
interpretations and atomism, and look at applications to the realm of dynamic
space-time theories. We then consider models of kinetic media in subspace
compatible with our understanding of light. From the equations governing the
propagation of light in subspace we can build a metric geometry...

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## Classical Gravity as an Eikonal Approximation to a Manifestly Lorentz Covariant Quantum Theory with Brownian Interpretation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/07/2004
Português

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We discuss in this Chapter a series of theoretical developments which
motivate the introduction of a quantum evolution equation for which the eikonal
approximation results in the geodesics of a four dimensional manifold. This
geodesic motion can be put into correspondence with general relativity. One
obtains in this way a quantum theory on a flat spacetime, obeying the rules of
the standard quantum theory in Lorentz covariant form, with a spacetime
dependent Lorentz tensor $g_{\mu\nu}$, somewhat analogous to a gauge field,
coupling to the kinetic terms. Since the geodesics predicted by the eikonal
approximation, with appropriate choice of $g_{\mu\nu}$, can be those of general
relativity, this theory provides a quantum theory which could be underlying to
classical gravitation, and coincides with it in this classical ray
approximation. In order to understand the possible origin of the structure of
this equation, we appeal to the approach of Nelson in constructing a
Schroedinger equation from the properties of Brownian motion. Extending the
notion of Browninan motion to spacetime in a covariant way, we show that such
an equation follows from correlations between spacetime dimensions in the
stochastic process.; Comment: 46 pages, PLain TeX. To be published in "Progress in General
Relativity and Quantum Cosmology Research". Hauppage (2004)

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## Introduction to Modern Canonical Quantum General Relativity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/10/2001
Português

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#General Relativity and Quantum Cosmology#High Energy Physics - Theory#Mathematical Physics#Mathematics - Functional Analysis#Mathematics - Operator Algebras#Mathematics - Symplectic Geometry#Quantum Physics

This is an introduction to the by now fifteen years old research field of
canonical quantum general relativity, sometimes called "loop quantum gravity".
The term "modern" in the title refers to the fact that the quantum theory is
based on formulating classical general relativity as a theory of connections
rather than metrics as compared to in original version due to Arnowitt, Deser
and Misner. Canonical quantum general relativity is an attempt to define a
mathematically rigorous, non-perturbative, background independent theory of
Lorentzian quantum gravity in four spacetime dimensions in the continuum. The
approach is minimal in that one simply analyzes the logical consequences of
combining the principles of general relativity with the principles of quantum
mechanics. The requirement to preserve background independence has lead to new,
fascinating mathematical structures which one does not see in perturbative
approaches, e.g. a fundamental discreteness of spacetime seems to be a
prediction of the theory providing a first substantial evidence for a theory in
which the gravitational field acts as a natural UV cut-off. An effort has been
made to provide a self-contained exposition of a restricted amount of material
at the appropriate level of rigour which at the same time is accessible to
graduate students with only basic knowledge of general relativity and quantum
field theory on Minkowski space.; Comment: 301 pages...

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## Combining general relativity and quantum theory: points of conflict and contact

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/10/2001
Português

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The issues related to bringing together the principles of general relativity
and quantum theory are discussed. After briefly summarising the points of
conflict between the two formalisms I focus on four specific themes in which
some contact has been established in the past between GR and quantum field
theory: (i) The role of planck length in the microstructure of spacetime (ii)
The role of quantum effects in cosmology and origin of the universe (iii) The
thermodynamics of spacetimes with horizons and especially the concept of
entropy related to spacetime geometry (iv) The problem of the cosmological
constant.; Comment: Invited Talk at "The Early Universe and Cosmological Observations: a
Critical Review", UCT, Cape Town, 23-25 July,2001; to appear in
Class.Quan.Grav

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## Noncommutative Unification of General Relativity and Quantum Mechanics. A Finite Model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/11/2003
Português

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We construct a model unifying general relativity and quantum mechanics in a
broader structure of noncommutative geometry. The geometry in question is that
of a transformation groupoid given by the action of a finite group G on a space
E. We define the algebra of smooth complex valued functions on the groupoid,
with convolution as multiplication, in terms of which the groupoid geometry is
developed. Owing to the fact that the group G is finite the model can be
computed in full details. We show that by suitable averaging of noncommutative
geometric quantities one recovers the standard space-time geometry. The quantum
sector of the model is explored in terms of the regular representation of the
groupoid algebra, and its correspondence with the standard quantum mechanics is
established.; Comment: 20 LaTex pages, General Relativity and Gravitation, in press

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## Classical and Quantum Cosmology of an Accelerating Model Universe with Compactification of Extra Dimensions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/02/2009
Português

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We study a $(4+D)$-dimensional Kaluza-Klein cosmology with a Robertson-Walker
type metric having two scale factors $a$ and $R$, corresponding to
$D$-dimensional internal space and 4-dimensional universe, respectively. By
introducing an exotic matter in the form of perfect fluid with an special
equation of state, as the space-time part of the higher dimensional
energy-momentum tensor, a four dimensional effective decaying cosmological term
appears as $\lambda \sim R^{-m}$ with $0 \leq m\leq 2$, playing the role of an
evolving dark energy in the universe. By taking $m=2$, which has some
interesting implications in reconciling observations with inflationary models
and is consistent with quantum tunneling, the resulting Einstein's field
equations yield the exponential solutions for the scale factors $a$ and $R$.
These exponential behaviors may account for the dynamical compactification of
extra dimensions and the accelerating expansion of the 4-dimensional universe
in terms of Hubble parameter, $H$. The acceleration of the universe may be
explained by the negative pressure of the exotic matter. It is shown that the
rate of compactification of higher dimensions as well as expansion of
4-dimensional universe depends on the dimension, $D$. We then obtain the
corresponding Wheeler-DeWitt equation and find the general exact solutions in
$D$-dimensions. A good correspondence between the solutions of classical
Einstein's equations and the solutions of quantum Wheeler-DeWitt equation in
any dimension...

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## The Chern-Simons Invariant as the Natural Time Variable for Classical and Quantum Cosmology

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We propose that the Chern-Simons invariant of the Ashtekar-Sen connection is
the natural internal time coordinate for classical and quantum cosmology. The
reasons for this are a number of interesting properties of this functional,
which we describe here. 1)It is a function on the gauge and diffeomorphism
invariant configuration space, whose gradient is orthogonal to the two physical
degrees of freedom, in the metric defined by the Ashtekar formulation of
general relativity. 2)The imaginary part of the Chern-Simons form reduces in
the limit of small cosmological constant, $\Lambda$, and solutions close to
DeSitter spacetime, to the York extrinsic time coordinate. 3)Small matter-field
excitations of the Chern-Simons state satisfy, by virtue of the quantum
constraints, a functional Schroedinger equation in which the matter fields
evolve on a DeSitter background in the Chern-Simons time. We then n propose
this is the natural vacuum state of the theory for $\Lambda \neq 0$. 4)This
time coordinate is periodic on the configuration space of Euclideanized
spacetimes, due to the large gauge transformations, which means that physical
expectation values for all states in non-perturbative quantum gravity will
satisfy the $KMS$ condition, and may then be interpreted as thermal states.
5)Forms for the physical hamiltonians and inner product which support the
proposal are suggested...

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## Conceptual issues in combining general relativity and quantum theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/12/1998
Português

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Points of conflict between the principles of general relativity and quantum
theory are highlighted. I argue that the current language of QFT is inadequete
to deal with gravity and review attempts to identify some of the features which
are likely to present in the correct theory of quantum gravity.; Comment: 6 pages, no figures. Invited article to be published in the
Festschrift volume to be brought out in honour of Professor J.V. Narlikar;
Editors: Naresh Dadhich and Ajit Kembhavi [Kluwer 99]

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## General Relativity and Quantum Mechanics in Five Dimensions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/02/2011
Português

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In 5D, I take the metric in canonical form and define causality by
null-paths. Then spacetime is modulated by a factor equivalent to the wave
function, and the 5D geodesic equation gives the 4D Klein-Gordon equation.
These results effectively show how general relativity and quantum mechanics may
be unified in 5D.

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## General relativity and cosmology

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/09/2015
Português

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#General Relativity and Quantum Cosmology#Astrophysics - Cosmology and Nongalactic Astrophysics#High Energy Physics - Phenomenology

This year marks the hundredth anniversary of Einstein's 1915 landmark paper
"Die Feldgleichungen der Gravitation" in which the field equations of general
relativity were correctly formulated for the first time, thus rendering general
relativity a complete theory. Over the subsequent hundred years physicists and
astronomers have struggled with uncovering the consequences and applications of
these equations. This contribution, which was written as an introduction to six
chapters dealing with the connection between general relativity and cosmology
that will appear in the two-volume book "One Hundred Years of General
Relativity: From Genesis and Empirical Foundations to Gravitational Waves,
Cosmology and Quantum Gravity," endeavors to provide a historical overview of
the connection between general relativity and cosmology, two areas whose
development has been closely intertwined.; Comment: 15 pages PDF, 4 figures, to appear as introductory chapter in "One
Hundred Years of General Relativity: From Genesis and Empirical Foundations
to Gravitational Waves, Cosmology and Quantum Gravity"

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## The Confrontation between General Relativity and Experiment

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/03/2014
Português

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#General Relativity and Quantum Cosmology#Astrophysics - Cosmology and Nongalactic Astrophysics#High Energy Physics - Theory

The status of experimental tests of general relativity and of theoretical
frameworks for analyzing them are reviewed and updated. Einstein's equivalence
principle (EEP) is well supported by experiments such as the Eotvos experiment,
tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP
and of the inverse square law are searching for new interactions arising from
unification or quantum gravity. Tests of general relativity at the
post-Newtonian level have reached high precision, including the light
deflection, the Shapiro time delay, the perihelion advance of Mercury, the
Nordtvedt effect in lunar motion, and frame-dragging. Gravitational-wave
damping has been detected in an amount that agrees with general relativity to
better than half a percent using the Hulse-Taylor binary pulsar, and a growing
family of other binary pulsar systems is yielding new tests, especially of
strong-field effects. Current and future tests of relativity will center on
strong gravity and gravitational waves.; Comment: 113 pages, 10 figures, an update of the 2006 Living Review
arXiv:gr-qc/0510072 ; submitted to Living Reviews in Relativity

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## The law of evolution of energy density in the universe imposed by quantum cosmology and its consequences

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/05/2004
Português

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The quantum model of homogeneous and isotropic universe filled with the
uniform scalar field is considered. This model predicts effective inverse
square-law dependence of the mean total energy density <\rho> on the
expectation value of cosmological scale factor where the averaging is
performed over the state with large quantum numbers. Such a law of decreasing
of <\rho> during the expansion of the universe allows to describe the observed
coordinate distances to type Ia supernovae and radio galaxies in the redshift
interval z = 0.01 - 1.8. A comparison with phenomenological models with the
cosmological constant (\Lambda CDM) and with zero dark energy component
(\Omega_{M} = 1) is made. It is shown that observed small deviations of the
coordinate distances to some sources from the predictions of above mentioned
simple quantum model can be explained by the fluctuations \delta a of the scale
factor about the average value . These fluctuations can arise due to finite
widths of quasistationary states in the early universe. During expansion the
fluctuations \delta a grow with time and manifest themselves in the form of
observed relative increase or decrease of coordinate distances. The amplitudes
of fluctuations \delta a/ calculated from observed positions of individual
supernovae are in good agreement with their estimations in quantum theory.
Possible consequences from the conclusions of quantum theory are discussed.; Comment: 17 pages...

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## Notes on Dilaton Quantum Cosmology

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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In these notes we address the canonical quantization of the cosmological
models which appear as solutions of the low energy effective action of closed
bosonic string theory (dilaton models). The analysis is restricted to the
quantization of the minisuperspace models given by homogeneous and isotropic
cosmological solutions. We study the different conceptual and technical
problems arising in the Hamiltonian formulation of these models as a
consequence of the presence of the so called Hamiltonian constraint. In
particular we address the problem of time in quantum cosmology, the
characterization of the symmetry under clock reversls arising from the
existence of a Hamiltonian constraint, and the problem of inposing boundary
conditions on the space of solutions of the Wheeler-DeWitt equation.; Comment: Invited article for the book "Trends in General Relativity and
Quantum Cosmology", Nova Science Publishers, NY (2005)

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## A scientometric study of General Relativity and Quantum Cosmology from 2000 to 2012

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Physics - History and Philosophy of Physics#Computer Science - Digital Libraries#General Relativity and Quantum Cosmology

2015 is the centennial of Einstein General Relativity. On this occasion, we
examine the General Relativity and Quantum Cosmology (GRQC) field of research
by analysing 38291 papers uploaded on the electronic archives arXiv.org from
2000 to 2012. We establish a map of the countries contributing to GRQC in 2012.
We determine the main journals publishing GRQC papers and which countries
publish in which journals. We find that more and more papers are written by
groups (instead of single) of authors with more and more international
collaborations. There are huge differences between countries. Hence Russia is
the country where most of papers are written by single authors whereas Canada
is one of the countries where the most of papers imply international
collaborations. We also study authors mobility, determining how some groups of
authors spread worldwide with time in different countries. The largest
mobilities are between USA-UK and USA-Germany. Countries attracting the most of
GRQC authors are Netherlands and Canada whereas those undergoing a brain drain
are Italy and India. There are few mobility between Europe and Asia contrarily
to mobility between USA and Asia.; Comment: 18 pages, 14 figures, to be published in Scientometrics

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