Background independent quantum gravity: A Status report
- A. Ashtekar, J. Lewandowski
- Physics
- 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…
Quantum Nature of the Big Bang: Improved dynamics
- A. Ashtekar, T. Pawłowski, 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…
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…
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…
Mathematical structure of loop quantum cosmology
- A. Ashtekar, M. Bojowald, J. Lewandowski
- Philosophy, Physics
- 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…
Asymptotically anti-de Sitter space-times
- A. Ashtekar, A. Magnon
- Mathematics
- 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…
Representation Theory of Analytic Holonomy C* Algebras
- A. Ashtekar, J. Lewandowski
- 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…
Quantum nature of the big bang: An analytical and numerical investigation
- A. Ashtekar, T. Pawłowski, 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…
Quantum Theory of Geometry II: Volume operators
- A. Ashtekar, J. Lewandowski
- Physics
- 10 November 1997
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, Uniwersytet…
Quantum nature of the big bang.
- A. Ashtekar, T. Pawłowski, Parampreet Singh
- PhysicsPhysical Review Letters
- 22 February 2006
The known results on the resolution of the big-bang singularity in loop quantum cosmology are significantly extended, and unlike in other approaches the quantum evolution is deterministic across the deep Planck regime.
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