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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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Quantum Nature of the Big Bang: Improved dynamics
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detailExpand
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Lectures on Non-Perturbative Canonical Gravity
Notes prepared in Collaboration with Ranjeet S Tate It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description ofExpand
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Loop Quantum Cosmology: A Status Report
Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the 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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Asymptotically anti-de Sitter space-times
The structure of the gravitational field at infinity of asymptotically anti-de Sitter space-time is analysed in detail using conformal techniques. It is found that the situation differs from that inExpand
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Quantum geometry of isolated horizons and black hole entropy
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admittingExpand
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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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Isolated horizons: Hamiltonian evolution and the first law
A framework was recently introduced to generalize black hole mechanics by replacing stationary event horizons with isolated horizons. That framework is significantly extended. The extension isExpand
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