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Topic: Euclidean quantum gravity

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Loop quantum gravity

Quantum gravity

	Quantum gravity - Wikipedia, the free encyclopedia
		Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity.
		Quantum field theory on curved (non-Minkowskian) backgrounds, while not a quantum theory of gravity, has shown that some of the core assumptions of quantum field theory cannot be carried over to curved spacetime, let alone to full-blown quantum gravity.
		Loop quantum gravity of Ashtekar, Smolin and Rovelli
	en.wikipedia.org /wiki/Quantum_gravity (1403 words)

	Quantum gravity: progress from an unexpected direction
		It has elements of both the quantum and the geometric approaches; and it is sufficiently different to irritate partisans of both camps.
		Quantum gravity, the as yet unconsummated marriage between quantum physics and Einstein's general relativity, is widely (though perhaps not universally) regarded as the single most pressing problem facing theoretical physics at the turn of the millennium.
		On the other hand, ``Lorentzian lattice quantum gravity'' has irritated both brane theorists and general relativists (and more than a few lattice physicists as well): It does not have, and does not seem to require, the complicated superstructure of supersymmetry and all the other technical machinery of brane theory/ string theory.
	www.phys.lsu.edu /mog/mog19/node12.html (796 words)

	Qgravity.org: Technical Summary of Loop Quantum Gravity (Site not responding. Last check: 2007-10-05)
		Loop quantum gravity provides a general framework for diffeomorphism invariant quantum field theories, within which there is a complete quantization of Einstein's theory of general relativity.
		Loop quantum gravity is a general framework for the construction and study of diffeomorphism invariant quantum field theories.
		Another possibility is to define the space of states in loop quantum gravity not from measures on a configuration space but as representations of a complete (in the sense that they coordinatize the kinematical phase space) set of observables.
	www.qgravity.org /loop (7364 words)

	Euclidean quantum gravity - Wikipedia, the free encyclopedia
		Euclidean quantum gravity refers to a Wick rotated version of quantum gravity, formulated as a quantum field theory.
		It is also assumed that the manifolds are compact, connected and boundaryless (i.e.
		Following the usual quantum field-theoretic formulation, the vacuum to vacuum amplitude is written as a functional integral over the metric tensor, which is now the quantum field under consideration.
	en.wikipedia.org /wiki/Euclidean_quantum_gravity (112 words)

	5 Calculations of Black Hole Entropy
		] in the context of Euclidean quantum gravity.
		A number of other entropy calculations that have been given within the formal framework of Euclidean quantum gravity also can be shown to be equivalent to the classical derivation (see [61] for further discussion).
		Thus, although the derivation of [50] and other related derivations give some intriguing glimpses into possible deep relationships between fl hole thermodynamics and Euclidean quantum gravity, they do not appear to provide any more insight than the classical derivation into accounting for the quantum degrees of freedom that are responsible for fl hole entropy.
	relativity.livingreviews.org /Articles/lrr-2001-6/node7.html (2339 words)

	Historical Notes: Quantum gravity
		That there should be quantum effects in gravity was already noted in the 1910s, and when quantum field theory began to develop in the 1930s, there were immediately attempts to apply it to gravity.
		The first idea was to represent gravity as a field that exists in flat spacetime, and by analogy with photons in quantum electrodynamics to introduce gravitons (at one point identified with neutrinos).
		Starting in the 1950s a rather different approach to quantum gravity involved trying to find a representation of the structure of spacetime in which a quantum analog of the Einstein equations could be obtained by the formal procedure of canonical quantization (see page 1062).
	www.wolframscience.com /reference/notes/1054a (1043 words)

	The discrete charm of quantum gravity
		ALL the Monte Carlo simulations you mention were studying theories of "Euclidean quantum gravity", where we take the Einstein-Hilbert action S for Riemannian metrics and do a discretized version of the path integral involving exp(-S).
		Once this is done, one obtains a theory of quantum gravity where space-time is fractal: the intrinsic Hausdorff dimension of usual 2d Euclidean quantum gravity is four, and not two.
		However, certain aspects of quantum space-time remain two-dimensional, exemplified by the fact that its so-called spectral dimension is equal to two.
	www.lns.cornell.edu /spr/2001-07/msg0033943.html (849 words)

	200 Quantum Gravity Links
		http://graham.main.nc.us/~bhammel/FCCR/qg.html An essay concerning the concept of quantum gravity ab initio and constraints on structural models for it that are imposed by the essential notions of general relativity and by quantum theory.
		http://simscience.org/membranes/advanced/essay/gravity_simulation1.html Simulating Quantum Gravity As we described earlier, one might imagine that on a very, very small scale, space may be a wild blur consisting of a combination of every imaginable kind of curvature.
		Topics in loop quantum gravity Norbert Grot, 1998 Gravitational radiation from fl hole spacetimes Luis Lehner, 1998 General Ralativity as a theory of null surfaces Simonetta Frittelli, 1995 On loop theoretic frameworks of quantum gravity...
	www.mysteries-megasite.com /main/bigsearch/quantum.html (3498 words)

	EUCLIDEAN QUANTUM GRAVITY (Site not responding. Last check: 2007-10-05)
		The Euclidean approach to Quantum Gravity was initiated almost 15 years ago in an attempt to understand the difficulties raised by the spacetime singularities of classical general relativity which arise in the gravitational collapse of stars to form fl holes and the entire universe in the Big Bang.
		An important motivation was to develop an approach capable of dealing with the nonlinear, non-perturbative aspects of quantum gravity due to topologically non-trivial spacetimes.
		This is a collection of survey lectures and reprints of some important lectures on the Euclidean approach to quantum gravity in which one expresses the Feynman path integral as a sum over Riemannian metrics.
	www.worldscibooks.com /physics/1301.htm (343 words)

	[No title]
		For the familiar quantum field theories in flat spacetime this requirement is usually satisfied, but in the case of quantum gravity the situation is in general much more complicated since the metric itself belongs to the dynamic variables of the theory.
		We may treat it, ``{\it a la} particle physics", like a normal quantum field theory (or possibly an effective low-energy theory \cite{don}) in which the background metric is fixed and the analytical continuation between the Euclidean and Minkowskian case is well defined.
		We know that in the quantum theory the gravitational force between two masses at rest is given in principle by eq.\ (\ref{ciaobis}) but that equation does not give us enough information to compute the average field, nor it ensures that in the quantum case an average field is well defined at all.
	www.amasci.com /freenrg/jhs.txt (8135 words)

	Citebase - Asymptotic Freedom and Euclidean Quantum Gravity (Site not responding. Last check: 2007-10-05)
		To investigate Euclidean quantum gravity effects in a fundamental length scenario, we simulate 4$d$ SU(2) lattice gauge theory on a dynamically coupled Regge skeleton.
		The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution.
		We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-lat/9209001 (1197 words)

	Spin networks, spin foams and loop quantum gravity
		Loop quantum gravity is a theory that results from the canonical quantization of general relativity.
		Quantum gravity is one of the focus areas at the newly founded Perimeter Institute in Waterloo, Ontario, Canada, which has recruited Lee Smolin as well as several other influential researchers in quantum gravity.
		Quantum gravity with a positive cosmological constant, 2002.
	jdc.math.uwo.ca /spin-foams (2271 words)

	Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity
		The synthesis of quantum theory and general relativity is thus the central unsolved problem of theoretical physics41; no one today can predict with confidence what will be the language and ontology, much less the content, of this synthesis, when and if it comes.
		Just as quantum mechanics informs us that the position and momentum of a particle are brought into being only by the act of observation, so quantum gravity informs us that space and time themselves are contextual, their meaning defined only relative to the mode of observation.
		Quantum physics, hadron bootstrap theory, complex number theory, and chaos theory share the basic assumption that reality cannot be described in linear terms, that nonlinear -- and unsolvable -- equations are the only means possible to describe a complex, chaotic, and non-deterministic reality.
	www.physics.nyu.edu /faculty/sokal/transgress_v2/transgress_v2_singlefile.html (12361 words)

	Luboš Motl's reference frame: Wick rotation
		Most of this text is about quantum mechanics and non-gravitational quantum field theory, but it is reasonable to believe that the path integral in the Euclidean spacetime is gonna be even more important in quantum gravity than it is in quantum field theory.
		Finally, in quantum cosmology the path integral in Euclidean spacetime is likely to become even more important than in quantum field theory, not less, and the HH state has been the first glimpse why it is so.
		Lorentzian quantum gravity models have been rigorously constructed in 1+1 and 2+1 dimensions, and in 3+1 dimensions, people are working with Lorentzian models, whether by canonical quantization or with lattice models.
	motls.blogspot.com /2005/02/wick-rotation.html (10447 words)

	Re: This Week's Finds in Mathematical Physics (Week 206)
		Loll's approach was to develop discretized models of Lorentzian quantum gravity where Wick rotation is justified, and then do calculations in the Euclidean realm and analytically continue back.
		Indeed, in 2+1 dimensional gravity (formulated as a Chern-Simons gauge theory), the Euclidean and Minkowskian theories are totally different; they are not related by Wick rotation.
		It was, actually, surprising that lattice gravity in 3 dimensions did not (heretofore) appear to have a continuum limit even though we knew perfectly well that there was a continuum theory of 3D quantum gravity.
	www.lns.cornell.edu /spr/2004-05/msg0061112.html (1722 words)

	Gravitational Anomalies
		The main points of our analysis are the following: coherent coupling between gravity and a Bose condensate; induced gravitational instability and "runaway" of the field, with modification of the static potential; density distribution of the superconducting charge carriers; energetic balance; effective equations for the field; existence of a threshold density.
		Some wonder how the effect is connected to the perturbative or non-perturbative dynamics of quantum gravity or its generalizations; others take for granted that there is an exotic effect at the basis of the anomalous coupling, and focus on phenomenological issues.
		Furthermore, we use the Euclidean formulation in order to exhibit the stabilizing effect of a negative cosmological term and the de-stabilizing effect of a positive comological term, but still in the context of a weak field approximation.
	www.meta-religion.com /Physics/Gravity/gravitational_anomalies_by_htc_s.htm (8746 words)

	Citebase - Critical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions (Site not responding. Last check: 2007-10-05)
		The phase transition between the Gravity and Antigravity phases turned out to be asymmetrical, so that we observed the scaling laws only when the Newton constant approached the critical value from perturbative side.
		Loop quantum gravity is a mathematically well-defined, non-perturbative and background...
		We study the average number of simplices $N'(r)$ at geodesic distance $r$ in the dynamical triangulation model of euclidean quantum gravity in four dimensions.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-lat/9204004 (1020 words)

	IGPG: Mohammad Akbar (Site not responding. Last check: 2007-10-05)
		I explored their roles in quantum gravity/cosmology by studying how they can possibly provide solutions to the semi-classical approximation of the Euclidean path-integral of quantum gravity for general Dirichlet type boundary data.
		This is the premier centre for loop quantum gravity, currently one of the two most popular schemes for quantum gravity.
		On the classical side of gravity (but complementing the quantum part of investigation), I am primarily interested in isolated and dynamical horizons --- a detailed, new mathematical framework for fl-hole physics that has been developed at this Institute years.
	gravity.phys.psu.edu /people/igpg_makbar.shtml (318 words)

	Bangalore quantum gravity meeting
		The topics covered a fairly wide range, from (2+1)-dimensional quantum gravity, loop gravity, lattice approaches and 3-dimensional topology to the quantum theory of fl holes and, in particular, the issues associated with fl hole entropy.
		Once more it became clear that, despite all differences to (3+1)-dimensions, (2+1)-dimensional gravity is an important and useful test bed to study concepts and expectations in quantum gravity.
		Anomaly free regularizations of the super-hamiltonian have been constructed, but there is still an ongoing debate as to its physical correctness, since it does not define a deformation of the classical constraint algebra and hence seems to reproduce the wrong classical limit.
	www.phys.lsu.edu /mog/mog11/node19.html (788 words)

	Oblique (Grubb-Gilkey-Smith) boundary value problem in gauge theories and quantum gravity on manifolds with boundary
		The requirement of the gauge invariance of the boundary value problem leads to the fact that the boundary conditions in gauge theories depend, generally, on the gauge fixing condition.
		Namely, a part of the quantum field, (in gravity - the spatial components of the metric perturbations), satisfies Dirichlet boundary conditions, i.e.
		This leads to the fact that the trace of the heat kernel, and, therefore, the zeta-function and the functional determinant are not well defined in the non-elliptic case.
	infohost.nmt.edu /~iavramid/cv/res01/node7.html (693 words)

	Re: Riemannian vs. Lorentzian quantum gravity
		In article <79mv2h$p03$1@crib.corepower.com>, Nathan Urban wrote: >I always thought Euclideanized theories (t->it) were the physically the >same as Lorentzian theories, just written in a different way, but from >what I've read lately it seems that they're not.
		In quantum mechanics and quantum field theory on flat spacetime, there are theorems relating "real time" to "imaginary time".
		In quantum field theory it's a bit harder, because quantum field theory incorporates special relativity, and in special relativity there is no distinguished "time variable" - the time variable changes when you do a Lorentz transformation.
	www.lns.cornell.edu /spr/1999-02/msg0014598.html (632 words)

	boundary (Site not responding. Last check: 2007-10-05)
		In quantum field theory one then deals with the Euclidean approach, and its application to quantum gravity relies heavily on the theory of elliptic operators on Riemannian manifolds.
		On the other hand, in the application to quantum gravity, since the boundary operator acquires new kernels responsible for the pseudo-differential nature of the boundary-value problem, one might hope to be able to recover a good elliptic theory under a wider variety of conditions.
		Boundary field theory is therefore highly relevant for understanding quantum cosmology, quantum gravity and the foundations of quantized gauge theories, and it has deep roots in global analysis and spectral geometry.
	www.na.infn.it /Theor/gruppoIV/boundary.html (1208 words)

	4d Quantum Gravity (Site not responding. Last check: 2007-10-05)
		Louis Crane and I have proposed a state sum model for quantum gravity in 4 dimensions.
		This can be transcribed into quantum theory using the notion of a relativistic spin network, which is a spin network for Spin(4).
		For the 4-simplex, this show that the quantum amplitude is determined by integrating a certain weighting over geometries for a 4-simplex.
	www.maths.nott.ac.uk /personal/jwb/qg.4d.html (491 words)

	Re: Hawkings pre-big bang dimensional state (Site not responding. Last check: 2007-10-05)
		Euclidean quantum gravity does not _merely_ Wick rotate from
		Osterwalder-Schrader reconstruction theorem, in quantum gravity it is
		Euclidean quantum gravity is analytically continued back to Lorentzian
	superstringtheory.com /forum/hawking/messages/133.html (401 words)

	Table of contents for Library of Congress control number 2002041704
		Euclidean quantum gravity: the view from 2002 Gary Gibbons 21.
		Quantum geometry and its ramifications Abhay Ashtekar 24.
		Quantum cosmology and eternal inflation A. Vilenkin 37.
	www.loc.gov /catdir/toc/cam031/2002041704.html (440 words)

	Not Even Wrong » Blog Archive » Hawking in Dublin (Site not responding. Last check: 2007-10-05)
		His argument is in Euclidean quantum gravity, which he describes as “the only sane way to do quantum gravity non-perturbatively”, something which some might disagree with.
		Well, at various points he is clearly arguing from the point of view of euclidean quantum gravity.
		It always seemed to me that in the absence of a real theory of quantum gravity, you can’t tell which if any of these proposals really makes sense.
	www.math.columbia.edu /~woit/blog/archives/000057.html (1265 words)

	IHES PREPRINT M/01/35 (Site not responding. Last check: 2007-10-05)
		We discuss quantitative properties of a class of non-computable functions which appear as partition functions in Quantum gravity and are also of interest to Riemannian Geometry.
		As an application we describe a mechanism in the framework of the Hartle-Hawking approach to Quantum Gravity that might make possible two phenomena.
		One of these phenomena (``experimental mathematics") is the potential possibility of verification of predicates of the first order set theory by physical measurements.
	www.ihes.fr /PREPRINTS/M01/Resu/resu-M01-35.html (96 words)

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