115 citations · 484 across the 9 of their papers we have counts for
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Symmetry Reduction of Loop Quantum Gravity
Johannes Brunnemann, Tim A. Koslowski
The relation between standard Loop Quantum Cosmology and full Loop Quantum Gravity fails already at the first nontrivial step: The configuration space of Loop Quantum Cosmology can…
Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity
Johannes Brunnemann, David Rideout
We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator in loop quantum gravity (LQG). These structures encode geome…
Properties of the Volume Operator in Loop Quantum Gravity I: Results
Johannes Brunnemann, David Rideout
We analyze the spectral properties of the volume operator of Ashtekar and Lewandowski in Loop Quantum Gravity, which is the quantum analogue of the classical volume expression for…
Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation
Johannes Brunnemann, David Rideout
The properties of the Volume operator in Loop Quantum Gravity, as constructed by Ashtekar and Lewandowski, are analyzed for the first time at generic vertices of valence greater th…
Spectral Analysis of the Volume Operator in Loop Quantum Gravity
J. Brunnemann, D. Rideout
We describe preliminary results of a detailed numerical analysis of the volume operator as formulated by Ashtekar and Lewandowski. Due to a simplified explicit expression for its m…
Unboundedness of Triad -- Like Operators in Loop Quantum Gravity
Johannes Brunnemann, Thomas Thiemann
In this paper we deliver the proofs for the claims, made in a companion paper, concerning the avoidance of cosmological curvature singularities in in full Loop Quantum Gravity (LQG…
On (Cosmological) Singularity Avoidance in Loop Quantum Gravity
Johannes Brunnemann, Thomas Thiemann
Loop Quantum Cosmology (LQC), mainly due to Bojowald, is not the cosmological sector of Loop Quantum Gravity (LQG). Rather, LQC consists of a truncation of the phase space of class…
Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity
Johannes Brunnemann, Thomas Thiemann
The Volume Operator plays a crucial role in the definition of the quantum dynamics of Loop Quantum Gravity (LQG). Efficient calculations for dynamical problems of LQG can therefore…