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A relation between the Barbero-Immirzi parameter and the standard model
General Relativity and Quantum Cosmology · Submitted 16 Feb 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It has been shown that Sakharov's induced, from the fields entering the standard model, Barbero-Immirzi parameter assumes, in the framework of euclidean formalism, the UV cutoff-independent value, 1/9.
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It has been shown that Sakharov's induced, from the fields entering the standard model, Barbero-Immirzi parameter assumes, in the framework of euclidean formalism, the UV cutoff-independent value, 1/9. The calculus uses the Schwinger's proper-time formalism, the Seeley-DeWitt heat-kernel expansion, and it is akin to the derivation of the ABJ chiral anomaly in space-time with torsion.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It has been shown that Sakharov's induced, from the fields entering the standard model, Barbero-Immirzi parameter assumes, in the framework of euclidean formalism, the UV cutoff-independent value, 1/9. | result 0.91 | 0.16 | 0.89 | asserted 1.00 |
| s1 | The calculus uses the Schwinger's proper-time formalism, the Seeley-DeWitt heat-kernel expansion, and it is akin to the derivation of the ABJ chiral anomaly in space-time with torsion. | method 1.00 | 0.67 | 0.04 | asserted 0.99 |
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Original abstract
It has been shown that Sakharov's induced, from the fields entering the standard model, Barbero-Immirzi parameter assumes, in the framework of euclidean formalism, the UV cutoff-independent value, 1/9. The calculus uses the Schwinger's proper-time formalism, the Seeley-DeWitt heat-kernel expansion, and it is akin to the derivation of the ABJ chiral anomaly in space-time with torsion.
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2 arXiv papers cite this in 2 sentences
What it cites · 12 sentences without a confident label
Contests 1 paper
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The effective action for the chiral (left-handed) lepton is of the following form [equation] Then, the chiral part of the $M^2$-regularized effective lagrangian density reads [ref] (there is a misprint in the coefficient in front of the NY term in the first reference of [ref] —that coefficient is twice bigger than in the second reference) [equation] where $a_1$ is the 1st Seeley–DeWitt coefficient [ref] , and the NY term $𝒩𝒴$ is defined by [equation] It appears, as mentioned earlier, that the NY term $𝒩𝒴$ dominates the chiral anomaly in space with torsion, i.e. [ref] [equation] where $O(1)$ means terms of the zeroth order in $M$.
Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion · Introduction · contest 0.72
Compares with 3 papers
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For example, exactly in the framework of the standard model, we insert the following numbers of fundamental modes: $N_0=4$ (Higgs), $N_1/2=45$, $N_1=12$, $N_l=3$ (neutrinos), yielding $γ=1/9≈0.11$, which is quite close to the (a bit obsolete) Ashtekar–Baez–Corichi–Krasnov value, $γ_abck=ln2/π√(3)≈0.13$ [ref] , [ref] (see [ref] , for a better estimation).
Black hole entropy from Quantum Geometry · Introduction · 0.97
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For example, exactly in the framework of the standard model, we insert the following numbers of fundamental modes: $N_0=4$ (Higgs), $N_1/2=45$, $N_1=12$, $N_l=3$ (neutrinos), yielding $γ=1/9≈0.11$, which is quite close to the (a bit obsolete) Ashtekar–Baez–Corichi–Krasnov value, $γ_abck=ln2/π√(3)≈0.13$ [ref] , [ref] (see [ref] , for a better estimation).
Black hole entropy in Loop Quantum Gravity · Introduction · 0.97
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For example, exactly in the framework of the standard model, we insert the following numbers of fundamental modes: $N_0=4$ (Higgs), $N_1/2=45$, $N_1=12$, $N_l=3$ (neutrinos), yielding $γ=1/9≈0.11$, which is quite close to the (a bit obsolete) Ashtekar–Baez–Corichi–Krasnov value, $γ_abck=ln2/π√(3)≈0.13$ [ref] , [ref] (see [ref] , for a better estimation).
Isolated Horizons: the Classical Phase Space · Introduction · 0.97
Cites as background 3 papers
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In the Holst extended action for gravity [ref] the BI parameter $γ$ resides in the additional term of the full (Holst) action.
Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action · Introduction · 0.98
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Namely, the NY term can be quantumly induced by dominant part of one-loop contributions coming from chiral matter fields.) One should stress that there is a known approach using the black-hole entropy to fix the value of the BI parameter $γ$ (see, e.g. [ref] ).
Black hole entropy from Quantum Geometry · Introduction · 0.89
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The Barbero–Immirzi (BI) parameter $γ$ is an a priori free parameter in the framework of the modern approach to canonical gravity (Ashtekar's formalism) [ref] .
Background Independent Quantum Gravity: A Status Report · Introduction · 1.00
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