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On Locality in Quantum General Relativity and Quantum Gravity

Prugovecki, Eduard
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 25/03/1996
Relevância na Pesquisa
125.66%
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

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

Vaugon, Michel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/12/2015
Relevância na Pesquisa
135.65%
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.

Structure, Individuality and Quantum Gravity

Stachel, John
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
115.68%
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...

Noncommutative Unification of General Relativity and Quantum Mechanics

Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/04/2005
Relevância na Pesquisa
135.66%
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

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

Lusanna, Luca
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/04/2004
Relevância na Pesquisa
125.66%
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...

Kinematic self-similar solutions in general relativity

Maeda, Hideki; Harada, Tomohiro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/05/2004
Relevância na Pesquisa
125.72%
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)

The Dynamic Space of General Relativity in Second Atomization

Saul, Lukas A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
125.74%
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...

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

Horwitz, Lawrence P.; Oron, Ori
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/07/2004
Relevância na Pesquisa
115.72%
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)

Introduction to Modern Canonical Quantum General Relativity

Thiemann, Thomas
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/10/2001
Relevância na Pesquisa
115.72%
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...

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

Padmanabhan, T.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/10/2001
Relevância na Pesquisa
135.68%
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

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

Heller, M.; Odrzygozdz, Z.; Pysiak, L.; Sasin, W.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/11/2003
Relevância na Pesquisa
135.66%
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

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

Darabi, F.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/02/2009
Relevância na Pesquisa
135.71%
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...

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

Smolin, Lee; Soo, Chopin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
115.7%
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...

Conceptual issues in combining general relativity and quantum theory

Padmanabhan, T.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/12/1998
Relevância na Pesquisa
135.62%
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]

General Relativity and Quantum Mechanics in Five Dimensions

Wesson, Paul S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/02/2011
Relevância na Pesquisa
135.62%
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.

General relativity and cosmology

Bucher, Martin; Ni, Wei-Tou
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/09/2015
Relevância na Pesquisa
115.8%
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"

The Confrontation between General Relativity and Experiment

Will, Clifford M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/03/2014
Relevância na Pesquisa
115.7%
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

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

Kuzmichev, V. E.; Kuzmichev, V. V.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/05/2004
Relevância na Pesquisa
125.67%

Notes on Dilaton Quantum Cosmology

Catren, Gabriel; Simeone, Claudio
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
125.67%
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)

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

Fay, Stephane; Gautrias, Sebastien
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
155.71%
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