Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings

Jonathan Engle

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Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings

Jonathan Engle

General Relativity and Quantum Cosmology · Submitted 24 Jan 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization.

how it is stated · asserted 0.99 read the record →

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arXiv IDgr-qc/0701132 (version 4)

Pith ID63DSPYXF, Pith's permanent record of this paper and its review

CitationJonathan Engle. "Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings." arXiv:gr-qc/0701132 (2007). https://pith.science/paper/63DSPYXF

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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What the abstract itself states, as probabilities: claims first 0.16 · states limitation 0.47 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.43 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop quantum gravity. Then, using certain holomorphic representations, a new class of embeddings, called b-embeddings, are constructed, following the ideas of [1]. We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization. In the b-embedding case, the classical analogues of these operators separate points in phase space. Embedding at the gauge and diffeomorphism invariant level is discussed briefly in the conclusions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity.	background 0.85	0.53	0.04	unclear 0.53
s1	First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop quantum gravity.	contribution 0.90	0.85	0.04	asserted 0.99
s2	Then, using certain holomorphic representations, a new class of embeddings, called b-embeddings, are constructed, following the ideas of [1].	contribution 0.70	0.87	0.05	asserted 1.00
s3	We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization.	contribution 0.57	0.94	0.20	asserted 0.99
s4	In the b-embedding case, the classical analogues of these operators separate points in phase space.	result 0.99	0.88	0.14	asserted 1.00
s5	Embedding at the gauge and diffeomorphism invariant level is discussed briefly in the conclusions.	limitation 0.50	0.67	0.09	asserted 0.55

What kind of paper the classifier reports this is: theoretical result 0.78 · evidence from proof or derivation 1.00.

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arXiv listing abstract v4

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full text
figures and tables
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop quantum gravity. Then, using certain holomorphic representations, a new class of embeddings, called b-embeddings, are constructed, following the ideas of [1]. We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization. In the b-embedding case, the classical analogues of these operators separate points in phase space. Embedding at the gauge and diffeomorphism invariant level is discussed briefly in the conclusions.

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Towards Spinfoam Cosmology
gr-qc 2010-03 conditional novelty 7.0 of 10

The loop-quantum-gravity spinfoam transition amplitude between homogeneous isotropic coherent states is annihilated by an operator whose classical limit is the Friedmann Hamiltonian constraint, at first order in a sin...
Anomaly freedom in perturbative loop quantum gravity
gr-qc 2008-06 conditional novelty 6.0 of 10

Non-trivial inverse-triad corrections can be implemented in anomaly-free effective constraints for cosmological perturbations, at the cost of adding counterterms whose coefficients are fixed by the requirement that th...

How the literature uses it

11 arXiv papers cite this in 12 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Cites it as background 8 papers

The issue of performing a symmetry reduction in loop quantum gravity directly at the quantum level has received much attention in recent years [ref] .

An embedding of loop quantum cosmology in (b, v) variables into a full theory context · Introduction · 1.00
The resulting models (see e.g. [ref] for cosmological case, and see e.g. [ref] for black hole case), regarded as some type of symmetry-reduced sectors of LQG, yield valuable insight into the full LQG theory, regardless of the debates on embedding them into the full LQG [ref] .

Reduced Phase Space Quantization of Black Holes: Path Integrals, and Effective Dynamics · Introduction · 0.89
Moreover LQC has been suffered from the long-standing issue on the relation with the full theory of LQG (see e.g. [ref] for some earlier works on this perspective).

Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity · Introduction · 0.84

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