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Background independent quantum gravity: A Status report
The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantumExpand
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Mathematical structure of loop quantum cosmology
Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the bigExpand
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Representation Theory of Analytic Holonomy C* Algebras
Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization ofExpand
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Quantum Theory of Geometry II: Volume operators
Abhay Ashtekar, Jerzy Lewandowski 1 Center for Gravitational Physics and Geometry Department of Physics, Penn State, University Park, PA 16802-6300, USA 2 Instytut Fizyki Teoretycznej, UniwersytetExpand
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Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
Quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphism constraint is solved. The space of solutions is equipped with an inner product that is shownExpand
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Differential geometry on the space of connections via graphs and projective limits
Abstract In a quantum mechanical treatment of gauge theories (including general relativity), one is led to consider a certain completion A G of the space A G of guage equivalent connections. ThisExpand
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Black-hole entropy from quantum geometry
Quantum geometry (the modern loop quantum gravity involving graphs and spin-networks instead of the loops) provides microscopic degrees of freedom that account for black-hole entropy. However, theExpand
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Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac:Expand
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Projective techniques and functional integration for gauge theories
A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is thenExpand
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Quantum theory of geometry: I. Area operators
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. RegulatedExpand
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