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General Relativity in terms of Dirac Eigenvalues
Giovanni Landi, Carlo Rovelli
The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of ``observables'' for general relativ…
On the quantization of the Null-Surface formulation of GR
Simonetta Frittelli, Carlos N. Kozameh, Ezra T. Newman +2
We define and discuss various quantum operators that describe the geometry of spacetime in quantum general relativity. These are obtained by combining the Null-Surface Formulation…
``Sum over Surfaces'' form of Loop Quantum Gravity
Michael P Reisenberger, Carlo Rovelli
We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry…
Relational Quantum Mechanics
Carlo Rovelli
I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the "measurement problem") could derive from the use of an incorrect notion,…
The complete spectrum of the area from recoupling theory in loop quantum gravity
Simonetta Frittelli, Luis Lehner, Carlo Rovelli
We compute the complete spectrum of the area operator in the loop representation of quantum gravity, using recoupling theory. This result extends previous derivations, which did no…
Loop Quantum Gravity and Black Hole Physics
Carlo Rovelli
I summarize the basic ideas and formalism of loop quantum gravity. I illustrate the results on the discrete aspects of quantum geometry and two applications of these results to bla…