Scalar material reference systems and loop quantum gravity

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 emphasized frequently. This idea has been picked up more recently in loop quantum gravity with the aim to pe...

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Bibliographic Details
Published in:Classical and quantum gravity 2015-07, Vol.32 (13), p.135015-135044
Main Authors: Giesel, K, Thiemann, T
Format: Article
Language:English
Subjects:
Dirac observables
Displays
Invariants
loop quantum gravity
Optimization
Quantization
Quantum gravity
Reference systems
Relativity
scalar material reference systems
Scalars
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Summary: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 emphasized frequently. This idea has been picked up more recently in loop quantum gravity with the aim to perform a reduced phase space quantization of the theory, thus possibly avoiding problems with the (Dirac) operator constraint quantization method for a constrained system. In this work, we review the models that have been studied on the classical and/or the quantum level and parametrize the space of theories considered so far. We then describe the quantum theory of a model that, to the best of our knowledge, has only been considered classically so far. This model could arguably be 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.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/32/13/135015