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Partial and complete observables for Hamiltonian constrained systems
We will pick up the concepts of partial and complete observables introduced by Rovelli in Conceptional Problems in Quantum Gravity, Birkhäuser, Boston (1991); Class Quant Grav, 8:1895 (1991); Phys
Partial and Complete Observables for Canonical General Relativity
In this work we will consider the concepts of partial and complete observables for canonical general relativity. These concepts provide a method to calculate Dirac observables. The central result of
Area?angle variables for general relativity
We introduce a modified Regge calculus for general relativity on a triangulated four-dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These
Broken) Gauge symmetries and constraints in Regge calculus
We will examine the issue of diffeomorphism symmetry in simplicial models of (quantum) gravity, in particular for Regge calculus. We find that for a solution with curvature there do not exist exact
A First Course in Loop Quantum Gravity
Students who are interested in quantum gravity usually face the difficulty of working through a large amount of prerequisite material before being able to deal with actual quantum gravity. A First
Phase space descriptions for simplicial 4D geometries
Starting from the canonical phase space for discretised (4d) BF–theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our
Time evolution as refining, coarse graining and entangling
We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that
A new vacuum for loop quantum gravity
We construct a new vacuum and representation for loop quantum gravity. Because the new vacuum is based on BF theory, it is physical for (2+1)-dimensional gravity, and much closer to the spirit of
Flux formulation of loop quantum gravity: Classical framework
We recently introduced a new representation for loop quantum gravity, which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay
A new realization of quantum geometry
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is