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Automorphisms in Loop Quantum Gravity
Benjamin Bahr, Thomas Thiemann
We investigate a certain distributional extension of the group of spatial diffeomorphisms in Loop Quantum Gravity. This extension, which is given by the automorphisms Aut(P) of the…
Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
K. Giesel, T. Thiemann
We perform a canonical, reduced phase space quantisation of General Relativity by Loop Quantum Gravity (LQG) methods. The explicit construction of the reduced phase space is made p…
Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order
K. Giesel, S. Hofmann, T. Thiemann +1
In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter…
Manifestly Gauge-Invariant General Relativistic Perturbation Theory: I. Foundations
K. Giesel, S. Hofmann, T. Thiemann +1
Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided e.g. by cosmic microwave anisotropy probes. A k…
Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
Benjamin Bahr, Thomas Thiemann
This is the second paper concerning gauge-invariant coherent states for Loop Quantum Gravity. Here, we deal with the gauge group SU(2), this being a significant complication compar…
Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
Benjamin Bahr, Thomas Thiemann
In this paper we investigate the properties of gauge-invariant coherent states for Loop Quantum Gravity, for the gauge group U(1). This is done by projecting the corresponding comp…
Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?
Bianca Dittrich, Thomas Thiemann
One of the celebrated results of Loop Quantum Gravity (LQG) is the discreteness of the spectrum of geometrical operators such as length, area and volume operators. This is an indic…