On the distribution of the eigenvalues of the area operator in loop quantum gravity

Barbero G., J. Fernando; Margalef Bentabol, Juan; Sánchez Villaseñor, Eduardo Jesús

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On the distribution of the eigenvalues of the area operator in loop quantum gravity

Author(s): Barbero G., J. Fernando; Margalef Bentabol, Juan; Sánchez Villaseñor, Eduardo Jesús

Publisher: IOP Publishing

Issued date: 2018-03-22

Citation: Barbero G., J. Fernando, Margalef-Bentabol, J. and Villaseñor, J.S. On the distribution of the eigenvalues of the area operator in loop quantum gravity. Classical and Quantum Gravity 35 (2018) 065008

ISSN: 0264-9381

DOI: https://doi.org/10.1088/1361-6382/aaabf9

xmlui.dri2xhtml.METS-1.0.item-contributor-funder: Ministerio de Economía y Competitividad (España)

Sponsor: This work has been supported by the Spanish MINECO research grants FIS2014-57387-C3-3-P and FIS2017-84440-C2-2-P. Juan Margalef-Bentabol is supported by 'la Caixa' and 'Residencia de Estudiantes' fellowships. One of the authors (JFBG) wants to thank Kirill Krasnov for a discussion that prompted the analysis of the different approximations based on the partition problem discussed in the paper. We also want to thank K Giesel, H Sahlmann, T Thiemann and the Quantum Gravity Group at the FAU University in Erlangen for interesting discussions and comments. Some of the computations and the plots have been done with the help of MathematicaTM.

Project: Gobierno de España. FIS2014-57387-C3-3-P
Gobierno de España. FIS2017-84440-C2-2-P

Keywords: Area spectrum in loop quantum gravity , Distribution of area eigenvalues , Hardy-Ramanujan Formula

URI: http://hdl.handle.net/10016/31379

Abstract:

We study the distribution of the eigenvalues of the area operator in loop quantum gravity concentrating on the part of the spectrum relevant for isolated horizons. We first show that the approximations relying on integer partitions are not sufficient to obtain [+]

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