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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… (More)

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… (More)

A functional calculus on the space of (generalized) connections was recently introduced without any reference to a background metric. It is used to continue the exploration of the quantum Riemannian… (More)

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… (More)

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… (More)

Black hole mechanics was recently extended by replacing the more commonly used event horizons in stationary space-times with isolated horizons in more general space-times (which may admit radiation… (More)

Geometrical structures intrinsic to non-expanding, weakly-isolated and isolated horizons are analysed and compared with structures which arise in other contexts within general relativity, e.g. at… (More)

In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker space-times arise as well-defined approximations to specific quantum geometries. We initiate the development of a quantum theory of test… (More)

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… (More)

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… (More)