The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
arXiv:hep-th/9907043 · doi:10.1088/0264-9381/17/15/311
Abstract
Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is investigated. The analysis requires a careful treatment of partial gauge fixing in the classical symmetry reduction and of the reinforcement of SU(2)-gauge invariance for the quantization of the area operator. The eigenvalues of that operator applied to spherically symmetric spin network states have the form A_n propor. sqrt{n(n+2)}, n=0,1,2..., giving A_n propor. n for large n. The result clarifies (and reconciles!) the relationship between the more complicated spectrum of the general (non-symmetric) area operator in loop quantum gravity and the old Bekenstein proposal that A_n propor. n.
16 pages, Latex
References in corpus (8)
- Loop Quantum Cosmology I: Kinematics
- Loop Quantum Cosmology II: Volume Operators
- Best Approximation to a Reversible Process in Black-Hole Physics and the Area Spectrum of Spherical Black Holes
- Group Theoretical Quantization of a Phase Space S^1 x R^+ and the Mass Spectrum of Schwarzschild Black Holes in D Space-Time Dimensions
- The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant
- Quantum Mechanics of a Black Hole
- Schwarzschild Black Hole Quantum Statistics from Z(2) Orientation Degrees of Freedom and its Relations to Ising Droplet Nucleation
- Abelian BF-Theory and Spherically Symmetric Electromagnetism
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