The Screen representation of spin networks. Images of 6j symbols and semiclassical features
arXiv:1405.0837 · doi:10.1007/978-3-642-39643-4_5
Abstract
This article presents and discusses in detail the results of extensive exact calculations of the most basic ingredients of spin networks, the Racah coefficients (or Wigner 6j symbols), exhibiting their salient features when considered as a function of two variables - a natural choice due to their origin as elements of a square orthogonal matrix - and illustrated by use of a projection on a square "screen" introduced recently. On these screens, shown are images which provide a systematic classification of features previously introduced to represent the caustic and ridge curves (which delimit the boundaries between oscillatory and evanescent behaviour according to the asymptotic analysis of semiclassical approaches). Particular relevance is given to the surprising role of the intriguing symmetries discovered long ago by Regge and recently revisited; from their use, together with other newly discovered properties and in conjunction with the traditional combinatorial ones, a picture emerges of the amplitudes and phases of these discrete wavefunctions, of interest in wide areas as building blocks of basic and applied quantum mechanics.
16 pages, 13 figures, presented at ICCSA 2013 13th International Conference on Computational Science and Application
References in corpus (1)
Cited by in corpus (4)
- The Screen representation of spin networks: 2D recurrence, eigenvalue equation for 6j symbols, geometric interpretation and Hamiltonian dynamics
- The screen representation of vector coupling coefficients or Wigner 3j symbols: exact computation and illustration of the asymptotic behavior
- Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective
- Quadrilaterals on the square screen of their diagonals: Regge symmetries of quantum-mechanical spin-networks and Grashof classical mechanisms of four-bar linkages