On the distribution of the eigenvalues of the area operator in loop quantum gravity Articles uri icon

publication date

  • March 2018

issue

  • 6

volume

  • 35

International Standard Serial Number (ISSN)

  • 0264-9381

Electronic International Standard Serial Number (EISSN)

  • 1361-6382

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 the asymptotic behaviour of the eigenvalue distribution for large areas. We then develop a method, based on Laplace transforms, that provides a very accurate solution to this problem. The representation that we get is valid for any area and can be used to study the asymptotics in the large area limit.

keywords

  • area spectrum in loop quantum gravity; distribution of area eigenvalues; hardy-ramanujan formula