General Relativity and Quantum Cosmology · arXiv:gr-qc/9705059 v1 · submitted 22 May 1997
The Immirzi parameter in quantum general relativity
The paper says
“This implies that there exists a one-parameter quantization ambiguity in quantum gravity, namely a free parameter that enters the construction of the quantum theory.”
from the abstract · picked out as the main claim by a classifier
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Abstract
Barbero has generalized the Ashtekar canonical transformation to a one-parameter scale transformation U(ι) on the phase space of general relativity. Immirzi has noticed that in loop quantum gravity this transformation alters the spectra of geometrical quantities. We show that U(ι) is a canonical transformation that cannot be implement unitarily in the quantum theory. This implies that there exists a one-parameter quantization ambiguity in quantum gravity, namely a free parameter that enters the construction of the quantum theory. The purpose of this letter is to elucidate the origin and the role of this free parameter.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.98
What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.19 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| Barbero has generalized the Ashtekar canonical transformation to a one-parameter scale transformation $U(\iota)$ on the phase space of general relativity. | background 1.00 | 0.05 | 0.03 | asserted 1.00 |
| Immirzi has noticed that in loop quantum gravity this transformation alters the spectra of geometrical quantities. | background 1.00 | 0.04 | 0.04 | asserted 1.00 |
| We show that $U(\iota)$ is a canonical transformation that cannot be implement unitarily in the quantum theory. | result 0.97 | 0.93 | 0.54 | asserted 1.00 |
| This implies that there exists a one-parameter quantization ambiguity in quantum gravity, namely a free parameter that enters the construction of the quantum theory. | interpretation 0.93 | 0.78 | 0.73 | asserted 0.98 |
| The purpose of this letter is to elucidate the origin and the role of this free parameter. | contribution 0.79 | 0.28 | 0.07 | asserted 0.73 |
What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.98
What was examined, and what was not
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- arXiv listing abstract v1
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- full text
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- references and citing sentences
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- P abstract
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- S sections
- T body sentences
- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,193 input tokens, $0.0002 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 10 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Quantum Geometry and Black Hole Entropy gr-qc · Oct 1997
- Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity gr-qc · Mar 2013
- SU(2) Loop Quantum Gravity seen from Covariant Theory gr-qc · Sep 2002
- Gauge Field Theory Coherent States (GCS) : I. General Properties hep-th · May 2000
- Quantum Theory of Geometry II: Volume operators gr-qc · Nov 1997
- Mixed state entanglement measures for open string geometry hep-th · Sep 2026
- Barbero-Immirzi field in canonical formalism of pure gravity gr-qc · Feb 2009
- Entanglement Entropy and Complexity of Multicomponent Universe from Holography hep-th · Jan 2026
- Holographic entanglement entropy and complexity for the cosmological braneworld model hep-th · May 2025
- Loop Quantum Gravity gr-qc · Oct 1997
How the literature uses it
22 arXiv papers cite this in 24 sentences
Papers citing it · 13 sentences without a confident label
Contests it 1 paper
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Although [ref] suggests a special quantization of a three dimensional non-relativistic particle of zero orbital momentum which is supposed to give rise to such an effect with the role of the area played by the kinetic energy, a correct analysis of this example given in [ref] shows the physical inadequacy of this quantization.
Critical Overview of Loops and Foams · Geometric operators · contest 0.89
Cites it as background 9 papers
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It is the parameter for a canonical transformation on the phase space, it does not have any effect on the classical equation of motion but it translates into a non-unitary transformation at the quantum level thus leading to non-equivalent quantization [ref] .
A Immirzi-like parameter for 3d quantum gravity · Introduction · 0.80
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At classical level, it relies on the Hamiltonian formulation of gravity through Ashtekar–Barbero canonical variables [ref] and features a real constant $$ (or $≡̱-1/$) called the Barbero–Immirzi (BI) parameter [ref] .
Barbero-Immirzi field in canonical formalism of pure gravity · Introduction · 0.95
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Now, these additional terms are driven by the so called Immirzi parameter $β$ [ref] , which is used in defining the Ashtekar variables and is related to a quantization ambiguity [ref] .
Big-bounce and future time singularity resolution in Bianchi I: the projective invariant Nieh-Yan case · Introduction · 0.98
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