2008/06/30 by Eugenio Bianchi · 106 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Compact operator #Computer science #Displacement operator #Eigenvalues and eigenvectors #Extension (predicate logic) #Immirzi parameter #Ladder operator #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Physics #Quantum #Quantum gravity #Quantum mechanics #Quantum state #Semiclassical physics #Spin foam #Spin network #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2008.08.013
published in Nuclear Physics B 807(3), 591-624 (Elsevier BV) · 33 pages, 12 figures; NPB version
openalex publication_date 2008/08/15 · arxiv created 2008/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.