Coherent states in the form of a quantum group

Zhe Chang

A set of deformed k-boson operators are defined and it is shown that the nonlinear transformations from the usual deformed oscillator operators to the deformed k-boson operators form an Abelian group. It is shown that the multiboson operators satisfy quantum Weyl–Heisenberg group. The generalized Holstein–Primakoff realizations in terms of these multibosons operators are used to define the quantum group-theoretic coherent states of SUq(1,1) and SUq(2). The uncertainties ΔX(k′,q) and ΔP(k′,q) with respect to those group-theoretic and generalized coherent states are computed explicitly and the results show that these coherent states are squeezed.

Alastair Brodlie

Zhe Chang

The author gives a generalization of the deformed oscillator and shows that it satisfies the quantum Weyl-Heisenberg group. The nonlinear transformations from the usual deformed oscillator operators to the deformed k-boson operators form an Abelian group. The generalized Holstein-Primakoff realizations in terms of these multiboson operators are used to define the quantum group-theoretic coherent states of SU q (1,1).

N. Aizawa, R. Chakrabarti, Swee-Ping Chia +2 more

The generalized coherent states (GCS) for two Lie groups are extend to quantum groups. The simplest examples for SUq(2) and Hq(1) are studied in some detail. It is shown that they enjoy analogous properties to classical counterparts such as resolution of unity. Especially, the SUq(2) GCS provide a natural description of q‐sphere in complex coordinates.

Ingemar Bengtsson, Karol Życzkowski