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2+1 Quantum Gravity with Barbero-Immirzi like parameter on Toric Spatial Foliation
General Relativity and Quantum Cosmology · Submitted 23 Sep 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The dimension of the Hilbert space is found to depend on the `Barbero-Immirzi' like parameter in an interesting fashion.
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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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The abstract, sentence by sentence
We consider gravity in 2+1 space-time dimensions, with negative cosmological constant and a `Barbero-Immirzi' (B-I) like parameter, when the space-time topology is of the form $ T^2 \times \mathbbm{R}$. The phase space structure, both in covariant and canonical framework is analyzed. Full quantization of the theory in the 'constrain first' approach reveals a finite dimensional physical Hilbert space. An explicit construction of wave functions is presented. The dimension of the Hilbert space is found to depend on the `Barbero-Immirzi' like parameter in an interesting fashion. Comparative study of this parameter in light of some of the recent findings in literarure for similar theories is presented.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider gravity in 2+1 space-time dimensions, with negative cosmological constant and a `Barbero-Immirzi' (B-I) like parameter, when the space-time topology is of the form $ T^2 \times \mathbbm{R}$. | contribution 0.56 | 0.57 | 0.05 | asserted 0.78 |
| s1 | The phase space structure, both in covariant and canonical framework is analyzed. | contribution 0.66 | 0.88 | 0.03 | asserted 0.95 |
| s2 | Full quantization of the theory in the 'constrain first' approach reveals a finite dimensional physical Hilbert space. | result 0.84 | 0.94 | 0.43 | asserted 1.00 |
| s3 | An explicit construction of wave functions is presented. | contribution 0.88 | 0.94 | 0.08 | asserted 1.00 |
| s4 | The dimension of the Hilbert space is found to depend on the `Barbero-Immirzi' like parameter in an interesting fashion. | result 1.00 | 0.95 | 0.42 | asserted 1.00 |
| s5 | Comparative study of this parameter in light of some of the recent findings in literarure for similar theories is presented. | contribution 0.93 | 0.68 | 0.08 | asserted 0.85 |
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The paper
Original abstract
We consider gravity in 2+1 space-time dimensions, with negative cosmological constant and a `Barbero-Immirzi' (B-I) like parameter, when the space-time topology is of the form $ T^2 \times \mathbbm{R}$. The phase space structure, both in covariant and canonical framework is analyzed. Full quantization of the theory in the 'constrain first' approach reveals a finite dimensional physical Hilbert space. An explicit construction of wave functions is presented. The dimension of the Hilbert space is found to depend on the `Barbero-Immirzi' like parameter in an interesting fashion. Comparative study of this parameter in light of some of the recent findings in literarure for similar theories is presented.
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How the literature uses it
2 arXiv papers cite this in 7 sentences
Papers citing it · 5 sentences without a confident label
Uses its method or tool 1 paper
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The rest of the prequantization technique can be analogously constructed as given in [ref] .
Consistent 3D Quantum Gravity on Lens Spaces · $ℋ _T^2$ · 0.93
Cites it as background 1 paper
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Although this can be found in various places, for example in [ref] , for completeness we would like to give a simple and short description of it.
Consistent 3D Quantum Gravity on Lens Spaces · $ℋ _T^2$ · 0.87
What it cites · 32 sentences without a confident label
Builds on 2 papers
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In the present work we consider a special case of such generalized CSG [ref] with a negative cosmological constant and a new parameter which immitates the Barbero Immirzi parameter of 3+1 gravity [ref] ; the possibility of this generalization also was hinted in the pioneering work [ref] .
Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action · Introduction · 0.85
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In the present work we consider a special case of such generalized CSG [ref] with a negative cosmological constant and a new parameter which immitates the Barbero Immirzi parameter of 3+1 gravity [ref] ; the possibility of this generalization also was hinted in the pioneering work [ref] .
Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity · Introduction · 0.85
Uses the method or tool of 2 papers
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On the other hand there is another simple way of finding the gauge invariant space especially for the case of genus 1, as outlined in [ref] , [ref] .
SL(2,R) Chern-Simons Theories with Rational Charges and Two-dimensional Conformal Field Theories · The physical phase space · 0.84
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On the other hand there is another simple way of finding the gauge invariant space especially for the case of genus 1, as outlined in [ref] , [ref] .
Chern-Simons Quantization of (2+1)-Anti-De Sitter Gravity on a Torus · The physical phase space · 0.84
Compares with 1 paper
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In terms of physical parameters we have l/G∈Q^+ l/Gγ∈Q^+ ⇒γ∈Q^+ which are slightly less restrictive than the results of the analysis done in [ref] $l/G∈Q^+$ and $l/Gγ∈N ⊂Q^+$.
Three-Dimensional Gravity Revisited · Results on the quantization of parameters · 0.95
Cites as support 1 paper
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In view of results from [ref] , where second order TMG was studied on an asymptotically AdS spacetime, we see that in order to make sense of all the graviton modes $γ$ should be restricted to 1.
Chiral Gravity in Three Dimensions · $γ→1$ limit in quantum theory · 0.97
Cites as background 10 papers
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We also wish to point out that in a later work [ref] , an explicit parameterization of the physical phase space for CSG on toric spatial foliation and negative cosmological constant was done.
Chern-Simons Quantization of (2+1)-Anti-De Sitter Gravity on a Torus · Introduction · 0.80
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A more general model for 2+1 gravity with negative cosmological constant was introduced by Mielke et al [ref] , [ref] and later studied extensively in [ref] , [ref] , [ref] , which without matter fields read: I = a I_1 +b I_2 + α_3 I_3 + α_4 I_4 where [equation] However this model does not reproduce the equations of motion EOM1 and EOM2 for arbitrary values of the parameters $a,b, α_3, α_4$.
Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity · Holst-like 2+1 Gravity as a Chern Simons theory · 0.86
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A more general model for 2+1 gravity with negative cosmological constant was introduced by Mielke et al [ref] , [ref] and later studied extensively in [ref] , [ref] , [ref] , which without matter fields read: I = a I_1 +b I_2 + α_3 I_3 + α_4 I_4 where [equation] However this model does not reproduce the equations of motion EOM1 and EOM2 for arbitrary values of the parameters $a,b, α_3, α_4$.
Asymptotic dynamics in 3D gravity with torsion · Holst-like 2+1 Gravity as a Chern Simons theory · 0.86
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