Year: 2007
Type: article
Abstract: 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.
Source: Classical and Quantum Gravity
Authors: N D Hari Dass, Manu Mathur
Institution: S.N. Bose National Centre for Basic Sciences
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1995822196