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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

1,207 92- PDF

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

630 51- PDF

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

322 40- PDF

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… Expand

463 27- PDF

Quantization of diffeomorphism invariant theories of connections with local degrees of freedom

- A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao, T. Thiemann
- Mathematics, Physics
- 12 April 1995

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 shown… Expand

544 26- PDF

Differential geometry on the space of connections via graphs and projective limits

- A. Ashtekar, J. Lewandowski
- Mathematics, Physics
- 8 December 1994

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. This… Expand

274 24- PDF

Black-hole entropy from quantum geometry

- M. Domagała, J. Lewandowski
- Physics
- 14 July 2004

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, the… Expand

323 18- PDF

Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras

- J. Lewandowski, A. Okołów, H. Sahlmann, T. Thiemann
- Mathematics, Physics
- 29 April 2005

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

263 18- PDF

Projective techniques and functional integration for gauge theories

- A. Ashtekar, J. Lewandowski
- Mathematics, Physics
- 17 November 1994

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 then… Expand

339 18- PDF

Quantum theory of geometry: I. Area operators

- A. Ashtekar, J. Lewandowski
- Physics
- 23 February 1996

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. Regulated… Expand

645 17- PDF

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