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Scalar Material Reference Systems and Loop Quantum Gravity

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arxiv 1206.3807 v2 pith:TW6KTS3R submitted 2012-06-17 gr-qc hep-th

Kristina Giesel , Thomas Thiemann This is my paper
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keywords quantumbeenconsideredgravityclassicaldescribediracloop
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In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasised frequently. This idea has been picked up more recently in Loop Quantum Gravity (LQG) with the aim to perform a reduced phase space quantisation of the theory thus possibly avoiding problems with the (Dirac) operator constraint quantisation method for constrained system. In this work, we review the models that have been studied on the classical and/or the quantum level and parametrise the space of theories so far considered. We then describe the quantum theory of a model that, to the best of our knowledge, so far has only been considered classically. This model could arguably called the optimal one in this class of models considered as it displays the simplest possible true Hamiltonian while at the same time reducing all constraints of General Relativity.

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Cited by 5 Pith papers

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  1. Quantum Reference Fields Transformations in Linearized Quantum Gravity

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    Extends quantum reference frames to quantum reference fields in linearized quantum gravity and derives unitary maps implementing relational gauge-invariant observables between quantum perspectives.

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    Backreactions from inhomogeneous modes on homogeneous geometry are significant and sensitive to Fock representation in this deparametrized second-order adiabatic calculation.

  3. Non-perturbative, background independent Fock representations for canonical quantum gravity

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  4. Localization and anomalous reference frames in gravity

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    Constructs a phase space for gravitational degrees of freedom on null ray segments with commuting localized observables via edge modes and dressing time, then introduces an effective classical theory with Virasoro def...

  5. Non-perturbative, background independent canonical quantum gravity in Fock representations

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    Existence of background-independent Fock representations for canonical quantum gravity with matter, producing a separable Hilbert space unlike LQG.

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