arXiv subjects
Publications and source records attributed to S. U. Park.
Various forms of the $q$-boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator. Both the one-component and the multicomponent $q$-bosons are discussed. As a byproduct, we obtain a new boson algebra having a shifted vacuum structure and define a global operatal $U(1)$ gauge transformation.
We consider a problem which may be viewed as an inverse one to the Schwinger realization of Lie algebra, and suggest a procedure of deforming the so-obtained algebra. We illustrate the method through a few simple examples extending Schwinger's $su(1,1)$ construction. As results, various q-deformed algebras are (re-)produced as well as their undeformed counterparts. Some extensions of the method are pointed out briefly.
The simple algebras of a dressed operator, which is composed of a dressing and a residual operators, are averaged following a proper statistics of the dressing one. In the Bose-Einstein statistics, a (fermionic) Calogero-Vasiliev oscillator, $q$-boson (fermion), and (fermionic) $su_q(1,1)$ are obtained for each bosonic (fermionic) residual operator. In the Fermi-Dirac statistics, new similar algebras are derived for each residual operator. Constructions of dual $q$-algebras, such as a dual Calogero-Vasiliev oscillator, a dual $q$-boson and a $su_q(2)$, and prospects are discussed.
We present the q-deformed ^M para-bose oscillators associated with (two-body) Calogero model.^M q-deformed coherent state is also constructed and its resolution of unity ^M is demonstrated.