The length operator in Loop Quantum Gravity

Details The length operator in Loop Quantum Gravity The length operator in Loop Quantum Gravity

2008-06-28

arxiv.org/abs/0806.4710v2

Nucl.Phys.B807:591-624,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, 12 figures; NPB version

Scientific paper

10.1016/j.nuclphysb.2008.08.013

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.

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