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31
Background independent quantum gravity: a status report
, 2004
"... The goal of this article is to present an introduction to loop quantum gravity —a background independent, nonperturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to pr ..."
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Cited by 259 (7 self)
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The goal of this article is to present an introduction to loop quantum gravity —a background independent, nonperturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird’s eye view of the present status of the subject, the article should also serve as a vehicle to enter the field and explore it in detail. To aid nonexperts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the article is essentially selfcontained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the article to a reasonable size, and to avoid overwhelming nonexperts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.
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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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. 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 dimensions (gauge invariance, discretization independence, etc.). In the second part we concentrate on the definition of the BarrettCrane model. We present the main results obtained in this framework from a critical perspective. Finally we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the BarrettCrane model in this framework and review the finiteness results obtained for both its Riemannian as well
Worldsheet formulations of gauge theories and gravity. talk given at the 7th Marcel Grossmann Meeting Stanford
, 1994
"... The evolution operator for states of gauge theories in the graph representation (closely related to the loop representation) is formulated as a weighted sum over worldsheets interpolating between initial and final graphs. As examples, lattice SU(2) BF and YangMills theories are expressed as worldsh ..."
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Cited by 45 (7 self)
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The evolution operator for states of gauge theories in the graph representation (closely related to the loop representation) is formulated as a weighted sum over worldsheets interpolating between initial and final graphs. As examples, lattice SU(2) BF and YangMills theories are expressed as worldsheet theories, and (formal) worldsheet forms of several continuum U(1) theories are given. It is argued that the world sheet framework should be ideal for representing GR, at least euclidean GR, in 4 dimensions, because it is adapted to both the 4diffeomorphism invariance of GR, and the discreteness of 3geometry found in the loop representation quantization of the theory. However, the weighting of worldsheets in GR has not yet been found. 1
The volume operator in discretized quantum gravity
 Phys. Rev. Lett
, 1995
"... We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a welldefined scalar product in this approach permits us to make definite statements about the hermiticity of quantum operators. We fi ..."
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Cited by 33 (11 self)
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We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a welldefined scalar product in this approach permits us to make definite statements about the hermiticity of quantum operators. We find that the spectrum of the volume operator is discrete, but that the nature of its eigenstates differs from that found in an earlier continuum treatment. 1 One of the most active branches of research into the quantization of 3+1dimensional gravity of the last few years has been the canonical, operatorbased framework of the socalled loop approach. It is nonperturbative in the sense that it is not a priori restricted to the study of geometries close to flat Minkowski space. Its basic variables are (nonlocal)
Knots and quantum gravity: progress and prospects
 TO APPEAR IN THE PROCEEDINGS OF THE SEVENTH MARCEL GROSSMAN MEETING ON GENERAL RELATIVITY, UNIVERSITY OF CALIFORNIA AT RIVERSIDE
, 1994
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Actions for gravity with generalizations: a review
, 1994
"... The search for a theory of quantum gravity has for a long time been almost fruitless. A few years ago, however, Ashtekar found a reformulation of Hamiltonian gravity, which thereafter has given rise to a new promising quantization project; the canonical Dirac quantization of Einstein gravity in term ..."
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The search for a theory of quantum gravity has for a long time been almost fruitless. A few years ago, however, Ashtekar found a reformulation of Hamiltonian gravity, which thereafter has given rise to a new promising quantization project; the canonical Dirac quantization of Einstein gravity in terms of Ahtekar’s new variables. This project has already given interesting results, although many important ingredients are still missing before we can say that the quantization has been successful. Related to the classical Ashtekar Hamiltonian, there have been discoveries regarding new classical actions for gravity in (2+1) and (3+1)dimensions, and also generalizations of Einstein’s theory of gravity. In the first type of generalization, one introduces infinitely many new parameters, similar to the conventional Einstein cosmological constant, into the theory. These generalizations are called ”neighbours of Einstein’s theory ” or ”cosmological constants generalizations”, and the theory has the same number of degrees of freedom, per point in spacetime, as the conventional Einstein theory. The second type is a gauge group generalization of Ashtekar’s Hamiltonian, and this theory has the correct number
New variables for classical and quantum gravity in all dimensions
 IV. Matter coupling”, Class. Quantum Grav
, 2013
"... Abstract We employ the techniques introduced in the companion papers ..."
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Cited by 14 (6 self)
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Abstract We employ the techniques introduced in the companion papers
Time, measurement and information loss in quantum cosmology, available on grqc/9301016
, 1993
"... A framework for a physical interpretation of quantum cosmology appropriate to a nonperturbative hamiltonian formulation is proposed. It is based on the use of matter fields to define a physical reference frame. In the case of the loop representation it is convenient to use a spatial reference frame ..."
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Cited by 11 (6 self)
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A framework for a physical interpretation of quantum cosmology appropriate to a nonperturbative hamiltonian formulation is proposed. It is based on the use of matter fields to define a physical reference frame. In the case of the loop representation it is convenient to use a spatial reference frame that picks out the faces of a fixed simplicial complex and a clock built with a free scalar field. Using these fields a procedure is proposed for constructing physical states and operators in which the problem of constructing physical operators reduces to that of integrating ordinary differential equations within the algebra of spatially diffeomorphism invariant operators. One consequence is that we may conclude that the spectra of operators that measure the areas of physical surfaces are discrete independently of the matter couplings or dynamics of the gravitational field. Using the physical observables and the physical inner product, it becomes possible to describe singularities, black holes and loss of information in a nonperturbative formulation of quantum gravity, without making reference to a background metric. While only a dynamical calculation can answer the question of whether quantum effects eliminate singularities, it is conjectured that, if they do not, loss of information is a likely result because the physical operator algebra that corresponds to measurements made at late times must be incomplete. Finally, I show that it is possible to apply Bohr’s original operational interpretation of quantum mechanics to quantum cosmology, so that one is free to use either a Copenhagen interpretation or a corresponding relative state interpretation in a canonical formulation of quantum cosmology. 1 SMOLIN: Time and measurement in quantum cosmology Contents