Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories

Thiemann, Thomas

doi:10.1088/0264-9381/15/5/012

Cited by 369 publications

(702 citation statements)

References 33 publications

(173 reference statements)

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“…Loop quantizations (using a densitized triad instead of the spatial metric) lead to discrete metric operators with zero in their discrete spectra, so that no direct inverse exists. Nevertheless, as proposed in [12,13], an inverse can be quantized in an indirect way, schematically writing q −1/2 = 2{q 1/2 , p q } and replacing the Poisson bracket by a commutator divided by i . A densely-defined operator results, but its spectrum differs from the expected q −1/2 n for small values of q n [14,15].…”

Section: Inverse-triad Correctionsmentioning

confidence: 99%

Minisuperspace models as infrared contributions

Bojowald

Brahma

2016

Phys. Rev. D

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A direct correspondence of quantum mechanics as a minisuperspace model for a self-interacting scalar quantum-field theory is established by computing, in several models, the infrared contributions to 1-loop effective potentials of Coleman-Weinberg type. A minisuperspace approximation rather than truncation is thereby obtained. By this approximation, the spatial averaging scale of minisuperspace models is identified with an infrared scale (but not a regulator or cut-off) delimiting the modes included in the minisuperspace model. Some versions of the models studied here have discrete space or modifications of the Hamiltonian expected from proposals of loop quantum gravity. They shed light on the question of how minisuperspace models of quantum cosmology can capture features of full quantum gravity. While it is shown that modifications of the Hamiltonian can well be described by minisuperspace truncations, some related phenomena such as signature change, confirmed and clarified here for modified scalar field theories, require at least a perturbative treatment of inhomogeneity beyond a strict minisuperspace model. The new methods suggest a systematic extension of minisuperspace models by a canonical effective formulation of perturbative inhomogeneity.

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Section: Inverse-triad Correctionsmentioning

confidence: 99%

Minisuperspace models as infrared contributions

Bojowald

Brahma

2016

Phys. Rev. D

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“…However, this refers to the classical speed of light, while a physical statement requires us to compare the velocity to the physical speed of light. This differs from the classical one because also the Maxwell Hamiltonian receives inverse volume corrections in loop quantum gravity [31]. In the regime of linear inhomogeneities such corrections have been computed in [32], and a derivation of the quantum corrected group velocity of electromagnetic waves, which we present in Sec.…”

Section: Inverse Volume Correctionsmentioning

confidence: 99%

Loop quantum gravity corrections to gravitational wave dispersion

2008

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Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based on Ashtekar's formulation of general relativity, including typical quantum gravity effects in the Hamiltonian constraint as they are expected from loop quantum gravity. This translates to corrections of the dispersion relation for gravitational waves. The main application here is the preservation of causality which is shown to be realized due to the absence of anomalies in the effective constraint algebra used.

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“…While such operators can be constructed in well-defined manners [32,27], their actions are highly involved on arbitrary states. Moreover, in particular the gravitational constraint usually changes the graph underlying a state it acts on because holonomies around closed loops are used to quantize curvature components.…”

Section: Aspects Of Loop Quantum Gravitymentioning

confidence: 99%

Loop quantum cosmology and inhomogeneities

2006

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Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of background independent quantizations in a setting accessible to explicit calculations of perturbations on a cosmological background. It is used here only for qualitative insights but can be extended with further more detailed input. One can thus see how several parameters occuring in homogeneous models appear from an inhomogeneous point of view. Their physical roles in several cases then become much clearer, often making previously unnatural choices of values look more natural by providing alternative physical roles. This also illustrates general properties of symmetry reduction at the quantum level and the roles played by inhomogeneities. Moreover, the constructions suggest a picture for gravitons and other metric modes as collective excitations in a discrete theory, and lead to the possibility of quantum gravity corrections in large universes.

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Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories

Cited by 369 publications

References 33 publications

Minisuperspace models as infrared contributions

Minisuperspace models as infrared contributions

Loop quantum gravity corrections to gravitational wave dispersion

Loop quantum cosmology and inhomogeneities

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