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research article

The theta parameter in loop quantum gravity: effects on quantum geometry and black hole entropy

Jimenez Rezende, Danilo  
•
Perez, Alejandro
2008
Physical Review D [1970-2015]

The precise analog of the theta-quantization ambiguity of Yang-Mills theory exists for the real SU(2) connection formulation of general relativity. As in the former case theta labels representations of large gauge transformations, which are super-selection sectors in loop quantum gravity. We show that unless theta=0, the (kinematical) geometric operators such as area and volume are not well defined on spin network states. More precisely the intersection of their domain with the dense set Cyl in the kinematical Hilbert space H of loop quantum gravity is empty. The absence of a well defined notion of area operator acting on spin network states seems at first in conflict with the expected finite black hole entropy. However, we show that the black hole (isolated) horizon area--which in contrast to kinematical area is a (Dirac) physical observable--is indeed well defined, and quantized so that the black hole entropy is proportional to the area. The effect of theta is negligible in the semiclassical limit where proportionality to area holds.

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Type
research article
DOI
10.1103/PhysRevD.78.084025
Author(s)
Jimenez Rezende, Danilo  
•
Perez, Alejandro
Date Issued

2008

Publisher

American Physical Society

Published in
Physical Review D [1970-2015]
Volume

78

Article Number

084025

Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
BMI  
Available on Infoscience
December 19, 2011
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/75824
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