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The quantum group SU<sub>q</sub>(2) and a q-analogue of the boson operators

Journal of Physics A Mathematical and General · 1989 · Vol. 22(18) · pp. L873–L878

Abstract

A new realisation of the quantum group SUq(2) is constructed by means of a q-analogue to the Jordan-Schwinger mapping, determining thereby both the complete representation structure and q-analogues to the Wigner and Racah operators. To achieve this realisation, a new elementary object is defined, a q-analogue to the harmonic oscillator. The uncertainty relation for position and momentum in a q-harmonic oscillator is quite unusual.

Algebraic structures and combinatorial models Advanced Topics in Algebra Black Holes and Theoretical PhysicsRealisationHarmonic oscillatorQuantum harmonic oscillatorGroup (periodic table)BosonPhysicsCreation and annihilation operatorsMomentum (technical analysis)Quantum mechanicsQuantum

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On the q oscillator and the quantum algebra su<sub>q</sub>(1,1)