Results 1  10
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2,159
Spin Foam Models for Quantum Gravity
, 2008
"... In this article we review the present status of the spin foam formulation of nonperturbative (background independent) quantum gravity. The article is divided in two parts. In the first part we present a general introduction to the main ideas emphasizing their motivations from various perspectives. R ..."
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Cited by 123 (7 self)
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. Riemannian 3dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for 4dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 343 (17 self)
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We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D
Black hole entropy from nearhorizon microstates,
 JHEP 9802,
, 1998
"... Abstract: Black holes whose nearhorizon geometries are locally, but not necessarily globally, AdS 3 (threedimensional antide Sitter space) are considered. Using the fact that quantum gravity on AdS 3 is a conformal field theory, we microscopically compute the black hole entropy from the asymptot ..."
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Cited by 284 (6 self)
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Abstract: Black holes whose nearhorizon geometries are locally, but not necessarily globally, AdS 3 (threedimensional antide Sitter space) are considered. Using the fact that quantum gravity on AdS 3 is a conformal field theory, we microscopically compute the black hole entropy from
Spin Foam Models for Quantum Gravity
, 2002
"... In this article we review the present status of the spin foam formulation of nonperturbative (background independent) quantum gravity. The article is divided in two parts. In the first part we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Ri ..."
Abstract
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. Riemannian 3dimensional gravity is used as a simple example to illustrate conceptual issues and main goals of the approach. The main features of the various existing models for 4dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four
Relativistic Spin Networks and Quantum Gravity
 J. Math Phys
, 1998
"... Abstract. Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) × SU(2). Relativistic quantum spins are related to the geometry of the 2dimensional faces of a 4simplex. This extends the idea of Ponzano and Regge that SU(2) spins are related to the geome ..."
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Cited by 180 (17 self)
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to the geometry of the edges of a 3simplex. This leads us to suggest that there may be a 4dimensional state sum model for quantum gravity based on relativistic spin networks which parallels the construction of 3dimensional quantum gravity from ordinary spin networks.
Quadratic nonRiemannian Gravity
"... We consider spacetime to be a connected real 4manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature ..."
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Cited by 2 (0 self)
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in curvature and study the resulting system of Euler–Lagrange equations. In the first part of the paper we look for Riemannian solutions, i.e. solutions whose connection is LeviCivita. We find two classes of Riemannian solutions: 1) Einstein spaces, and 2) spacetimes with metric of a ppwave and parallel
On the Gauge Aspects of Gravity
 in the Proc. of the 14th Course of the School of Cosmology and Gravitation on Quantum Gravity
, 1996
"... We give a short outline, in Sec. 2, of the historical development of the gauge idea as applied to internal (U(1), SU(2),...) and external (R 4, SO(1, 3),...) symmetries and stress the fundamental importance of the corresponding conserved currents. In Sec. 3, experimental results with neutron interfe ..."
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Cited by 66 (12 self)
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to gauge the fourdimensional affine group R 4 ⊃ × GL(4, R) or its Poincaré subgroup R 4 ⊃ × SO(1, 3). We briefly report on these results in Sec. 6 (metricaffine geometry) and in Sec. 7 (metricaffine field equations (111, 112, 113)). Finally, in Sec. 8, we collect some models, currently under discussion
The dS/CFT correspondence
 JHEP
, 2001
"... A holographic duality is proposed relating quantum gravity on dSD (Ddimensional de Sitter space) to conformal field theory on a single SD−1 ((D1)sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I + (the future bou ..."
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Cited by 196 (7 self)
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A holographic duality is proposed relating quantum gravity on dSD (Ddimensional de Sitter space) to conformal field theory on a single SD−1 ((D1)sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I + (the future
The structure of complete stable minimal surfaces in 3manifolds of nonnegative scalar curvature.
 Comm. Pure Appli. Math.
, 1980
"... The purpose of this paper is to study minimal surfaces in threedimensional manifolds which, on each compact set, minimize area up to second order. If M is a minimal surface in a Riemannian threemanifold N, then the condition that M be stable is expressed analytically by the requirement that o n a ..."
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Cited by 192 (1 self)
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The purpose of this paper is to study minimal surfaces in threedimensional manifolds which, on each compact set, minimize area up to second order. If M is a minimal surface in a Riemannian threemanifold N, then the condition that M be stable is expressed analytically by the requirement that o n
Euclidean Gravity.
, 1996
"... In the context of Ddimensional Euclidean gravity, we define the natural generalisation to Ddimensions of the selfdual YangMills equations, as duality conditions on the curvature 2form of a Riemannian manifold. Solutions to these selfduality equations are provided by manifolds of SU(2),SU(3),G2 ..."
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In the context of Ddimensional Euclidean gravity, we define the natural generalisation to Ddimensions of the selfdual YangMills equations, as duality conditions on the curvature 2form of a Riemannian manifold. Solutions to these selfduality equations are provided by manifolds of SU(2),SU(3),G
Results 1  10
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2,159