On Loop States in Loop Quantum Gravity

Abstract

We explicitly construct and characterize all possible independent loop states in 3+1 dimensional loop quantum gravity by regulating it on a 3-d 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 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.

12 pages, 3 figures, the version to be published in Classical and Quantum Gravity

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Cited by in corpus (8)

• Flipped spinfoam vertex and loop gravity
• Emergence of helicity +/- 2 modes (gravitons) from qubit models
• SU(N) Irreducible Schwinger Bosons
• Prepotential formulation of SU(3) lattice gauge theory
• Loop Approach to Lattice Gauge Theories
• Irreducible SU(3) Schwinger Bosons
• Canonical Transformations and Loop Formulation of SU(N) Lattice Gauge Theories
• Invariants, Projection Operators and $SU(N)\times SU(N)$ Irreducible Schwinger Bosons