Developments on the Jordan-Schwinger construction and contraction for the $s{u}_q(2)$

Abstract

The contraction and Jordan-Schwinger construction connect the $su(2)$ and the heisenberg algebra, going in oposite directions. This persists in the q-deformed cases, but in a slightly different way. This work investigates this further, discussing some details and results found in the litterature and presenting some new ones, including a non-linear expression that leads the contraction back to the original q-boson algebra used in the Jordan-Schwinger construction.

References in corpus (5)

• Quantum Field Theory on Noncommutative Spaces
• Field Theory on the q-deformed Fuzzy Sphere II: Quantization
• Wigner Oscillators, Twisted Hopf Algebras and Second Quantization
• Generalized Deformed Commutation Relations with Nonzero Minimal Uncertainties in Position and/or Momentum and Applications to Quantum Mechanics
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation