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Title: {theta} parameter in loop quantum gravity: Effects on quantum geometry and black hole entropy

Abstract

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 superselection 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.

Authors:
;  [1]
  1. Centre de Physique Theorique, Campus de Luminy, 13288 Marseille (France)
Publication Date:
OSTI Identifier:
21254450
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 78; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.78.084025; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; ENTROPY; GAUGE INVARIANCE; GENERAL RELATIVITY THEORY; HILBERT SPACE; QUANTIZATION; QUANTUM GRAVITY; SEMICLASSICAL APPROXIMATION; SPIN; SU-2 GROUPS; YANG-MILLS THEORY

Citation Formats

Rezende, Danilo Jimenez, and Perez, Alejandro. {theta} parameter in loop quantum gravity: Effects on quantum geometry and black hole entropy. United States: N. p., 2008. Web. doi:10.1103/PHYSREVD.78.084025.
Rezende, Danilo Jimenez, & Perez, Alejandro. {theta} parameter in loop quantum gravity: Effects on quantum geometry and black hole entropy. United States. doi:10.1103/PHYSREVD.78.084025.
Rezende, Danilo Jimenez, and Perez, Alejandro. Wed . "{theta} parameter in loop quantum gravity: Effects on quantum geometry and black hole entropy". United States. doi:10.1103/PHYSREVD.78.084025.
@article{osti_21254450,
title = {{theta} parameter in loop quantum gravity: Effects on quantum geometry and black hole entropy},
author = {Rezende, Danilo Jimenez and Perez, Alejandro},
abstractNote = {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 superselection 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.},
doi = {10.1103/PHYSREVD.78.084025},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 78,
place = {United States},
year = {2008},
month = {10}
}