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Background independent quantum gravity: A Status report

- A. Ashtekar, J. Lewandowski
- Physics, Mathematics
- 5 April 2004

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 quantum… Expand

Quantum Nature of the Big Bang: Improved dynamics

- A. Ashtekar, T. Pawlowski, Parampreet Singh
- Physics
- 10 July 2006

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 detail… Expand

Lectures on Non-Perturbative Canonical Gravity

- A. Ashtekar
- Physics
- 1991

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 of… Expand

Loop Quantum Cosmology: A Status Report

- A. Ashtekar, Parampreet Singh
- Physics
- 3 August 2011

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 quantum… Expand

Mathematical structure of loop quantum cosmology

- A. Ashtekar, M. Bojowald, J. Lewandowski
- Physics, Mathematics
- 21 April 2003

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 big… Expand

Representation Theory of Analytic Holonomy C* Algebras

- A. Ashtekar, J. Lewandowski
- Physics, Mathematics
- 7 November 1993

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 of… Expand

Asymptotically anti-de Sitter space-times

- A. Ashtekar, A. Magnon
- Physics
- 11 July 1984

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 in… Expand

Quantum nature of the big bang: An analytical and numerical investigation

- A. Ashtekar, T. Pawlowski, Parampreet Singh
- Physics
- 4 April 2006

Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both… Expand

Isolated and Dynamical Horizons and Their Applications

- A. Ashtekar, B. Krishnan
- Physics, MedicineLiving reviews in relativity
- 13 July 2004

TLDR

Quantum geometry of isolated horizons and black hole entropy

- A. Ashtekar, J. Baez, K. Krasnov
- Physics
- 29 May 2000

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, admitting… Expand

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