Jerzy Lewandowski

TL;DR: Loop quantum gravity as discussed by the authors is a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry.

TL;DR: In this article, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has been made explicit, thereby providing a firmer mathematical and conceptual foundation to the subject.

TL;DR: In this article, a functional calculus for quantum geometry is developed for a fully nonperturbative treatment of quantum gravity, which is used to begin a systematic construction of a quantum theory of geometry, and Regulated operators corresponding to 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states.

TL;DR: In this article, a quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphicism constraint is solved and the space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions.

TL;DR: In this article, a functional calculus is used to construct a quantum theory of geometry, where the fundamental excitations of quantum geometry are 1-dimensional, rather like polymers, and the 3-dimensional continuum geometry emerges only on coarse graining.