The length operator in Loop Quantum Gravity

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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.

Original languageEnglish (US)
Pages (from-to)591-624
Number of pages34
JournalNuclear Physics B
Issue number3
Publication statusPublished - Feb 1 2009


All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

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