The length operator in Loop Quantum Gravity
arXiv:0806.4710 · doi:10.1016/j.nuclphysb.2008.08.013
Abstract
The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity - the length operator. We describe its quantum geometrical meaning and derive some of its properties. In particular we show that the operator has a discrete spectrum and is diagonalized by appropriate superpositions of spin network states. A series of eigenstates and eigenvalues is presented and an explicit check of its semiclassical properties is discussed.
33 pages, 12 figures; NPB version
References in corpus (4)
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- The complete LQG propagator: II. Asymptotic behavior of the vertex
- The perturbative Regge-calculus regime of Loop Quantum Gravity
- Comment on "Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?" by B. Dittrich and T. Thiemann