A new basis on the state space of non-perturbative quantum gravity is introduced that allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation.Expand

The quantization of a simple dynamical system in which a unitary time evolution appears only within a certain approximation is studied in detail. The probabilistic interpretation of quantum mechanics… Expand

The basics of the loop representation of quantum gravity are summarized and the main aspects of the formalism are described, including its latest developments, in a reorganized and consistent form.Expand

A new represenatation for quantum general relativity is described, which is defined in terms of functionals of sets of loops in three-space. In this representation exact solutions of the quantum… Expand

The results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics.Expand

It is shown that a natural extension of canonical Heisenberg-picture quantum mechanics is well defined and can be used to describe the "non-Schr\"odinger regime," in which a fundamental time variable is not defined.Expand

This work argues that for a (macroscopically) Schwarzschild black hole this ensemble is formed by horizons with the same area, and obtains a statistical entropy proportional to the area, as in the Bekenstein-Hawking formula.Expand

A quantum Hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop… Expand

The general form that a nonperturbative quantum theory of gravity should have is discussed, and it is argued that this should be given by a generalization of Atiyah's topological quantum-field-theory axioms.Expand

It is shown that there exist quantum states which approximate a given metric at large scales, but such states exhibit a discrete structure at the Planck scale.Expand