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Quantum-Only Metrics in Spherically Symmetric Gravity

Faculty of Science and Technology, Free University of Bozen-Bolzano, 39100 Bolzano, Italy
Quantum Rep. 2020, 2(2), 314-325; https://doi.org/10.3390/quantum2020021
Received: 12 May 2020 / Revised: 7 June 2020 / Accepted: 16 June 2020 / Published: 18 June 2020
The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to reduce the effective dimensionality, we have performed a Monte Carlo simulation of the path integral with transition probability e β | S | . Although this choice does not allow to reproduce the full dynamics, it does lead us to find a large ensemble of metric configurations having action | S | ħ by several magnitude orders. These vacuum fluctuations are strong deformations of the flat space metric (for which S = 0 exactly). They exhibit a periodic polarization in the scalar curvature R. In the simulation we fix a length scale L and divide it into N sub-intervals. The continuum limit is investigated by increasing N up to 10 6 ; the average squared action S 2 is found to scale as 1 / N 2 and thermalization of the algorithm occurs at a very low temperature (classical limit). This is in qualitative agreement with analytical results previously obtained for theories with stabilized conformal factor in the asymptotic safety scenario. View Full-Text
Keywords: quantum gravity; path integral; lattice field theory; Metropolis algorithm quantum gravity; path integral; lattice field theory; Metropolis algorithm
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MDPI and ACS Style

Modanese, G. Quantum-Only Metrics in Spherically Symmetric Gravity. Quantum Rep. 2020, 2, 314-325. https://doi.org/10.3390/quantum2020021

AMA Style

Modanese G. Quantum-Only Metrics in Spherically Symmetric Gravity. Quantum Reports. 2020; 2(2):314-325. https://doi.org/10.3390/quantum2020021

Chicago/Turabian Style

Modanese, Giovanni. 2020. "Quantum-Only Metrics in Spherically Symmetric Gravity" Quantum Reports 2, no. 2: 314-325. https://doi.org/10.3390/quantum2020021

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