2006/11/30 by N. D. Hari Dass, N D Hari Dass, Manu Mathur
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Boson #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Harmonic oscillator #Immirzi parameter #Loop (graph theory) #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Operator (biology) #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/24/9/002
published as Class.Quant.Grav.24:2179-2192,2007 · 12 pages, 3 figures, the version to be published in Classical and Quantum Gravity
arxiv created 2007/03/21 · openalex publication_date 2007/04/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We explicitly construct and characterize all possible independent loop states in (3 + 1)-dimensional loop-quantum gravity by regulating it on a 3D regular lattice in the Hamiltonian formalism. These loop states, characterized by the (dual) angular momentum quantum numbers, describe SU (2) rigid rotators on the links of the lattice. The loop states are constructed using the Schwinger bosons which are harmonic oscillators in the fundamental (spin half) representation of SU (2). Using the generalized Wigner–Eckart theorem, we compute the matrix elements of the volume operator in the loop basis. Some simple loop eigenstates of the volume operator are explicitly constructed.