2021
DOI: 10.48550/arxiv.2112.14781
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Numerical analysis of the self-energy in covariant Loop Quantum Gravity

Pietropaolo Frisoni,
Francesco Gozzini,
Francesca Vidotto

Abstract: We study numerically the first order radiative corrections to the self-energy, in covariant loop quantum gravity. We employ the recently developed sl2cfoam-next spinfoam amplitudes library, and some original numerical methods. We analyze the scaling of the divergence with the infrared cutoff, for which previous analytical estimates provided widely different lower and upper bounds. Our findings suggest that the divergence is approximately linear in the cutoff. We also investigate the role of the Barbero-Immirzi… Show more

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Cited by 3 publications
(22 citation statements)
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“…The effect of orientation change of the (4jm) symbols cancels exactly the effect of orientation change of the reduced density matrices of SL(2, C), as we discuss in Appendix B. Using this definition, we can write (13) in terms of the booster functions as:…”
Section: How-to Compute the Eprl Vertex Amplitudesmentioning
confidence: 97%
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“…The effect of orientation change of the (4jm) symbols cancels exactly the effect of orientation change of the reduced density matrices of SL(2, C), as we discuss in Appendix B. Using this definition, we can write (13) in terms of the booster functions as:…”
Section: How-to Compute the Eprl Vertex Amplitudesmentioning
confidence: 97%
“…Recently [13] introduced an extrapolation scheme to overcome the enormous computational cost represented by indefinitely increasing ∆l, possibly making a massive step forward in the computability of the spin foam amplitude. The extrapolation algorithm was used to calculate the self-energy spinfoam amplitude (see [50,43]), which is a divergent amplitude since it contains a bubble.…”
Section: How-to Divide the Eprl Transition Amplitudesmentioning
confidence: 99%
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