Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective

Abstract

A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.

15 pages, 10 figures, presented at ICCSA 2014, 14th International Conference on Computational Science and Applications

References in corpus (10)

• Semiclassical analysis of Wigner $3j$-symbol
• The equitable Racah algebra from three su(1,1) algebras
• 3nj Morphogenesis and Semiclassical Disentangling
• Uniform Semiclassical Approximation for the Wigner $6j$ Symbol in Terms of Rotation Matrices
• Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials
• The Screen representation of spin networks: 2D recurrence, eigenvalue equation for 6j symbols, geometric interpretation and Hamiltonian dynamics
• The Screen representation of spin networks. Images of 6j symbols and semiclassical features
• Quantum states of elementary three-geometry
• The volume operator for spin networks with planar or cylindrical symmetry
• The volume operator for singly polarized gravity waves with planar or cylindrical symmetry

Cited by in corpus (2)

• The screen representation of vector coupling coefficients or Wigner 3j symbols: exact computation and illustration of the asymptotic behavior
• Quadrilaterals on the square screen of their diagonals: Regge symmetries of quantum-mechanical spin-networks and Grashof classical mechanisms of four-bar linkages