What question did this study set out to answer?

The study aims to derive an effective fermionic mass operator using loop quantum gravity principles.

March 29, 2026Open Access

Kerr-Planck Cosmology in Loop Quantum Gravity: Three Fermionic Generations from Winding Modes in the EPRL Amplitude of a Kerr-Planck

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The study aims to derive an effective fermionic mass operator using loop quantum gravity principles.
Derived the fermionic mass operator from the Einstein-Cartan action coupled with Dirac fields.
Utilized the covariant EPRL spin-foam amplitude with a Kerr-Planck Euclidean core.
Expanded fermions in winding modes around a compact geometry, leading to an effective action.
Minimized the effective action to select stable winding modes, applying the Atiyah-Patodi-Singer index.
Identified three stable winding modes (n = 1, 2, 3) that contribute to fermionic generation.
Demonstrated that the derived Yukawa couplings reproduce the observed hierarchy of fermion masses without free parameters.
Showed minimization of the effective action leads to exponentially separated mass terms for fermions.

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Implication

This research demonstrates three fermionic generations arise from winding modes in a novel cosmological framework, suggesting underlying principles of mass generation.

Cite This Study

Carlos Javier Díaz Curiel (2026) studied this question.

synapsesocial.com/papers/69c8c43ede0f0f753b39ef77 https://doi.org/10.5281/zenodo.19251522

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Implication

This research demonstrates three fermionic generations arise from winding modes in a novel cosmological framework, suggesting underlying principles of mass generation.

Kerr-Planck Cosmology in Loop Quantum Gravity: Three Fermionic Generations from Winding Modes in the EPRL Amplitude of a Kerr-Planck

Key Points

Discussion

Implication

Cite This Study

Kerr-Planck Cosmology in Loop Quantum Gravity: Three Fermionic Generations from Winding Modes in the EPRL Amplitude of a Kerr-Planck

Key Points

Discussion

Implication

Cite This Study

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