Generalized Coherent States Associated with the $C_λ$-Extended Oscillator
C. Quesne
备注：
7 pages, LaTeX2e, no figure, communication at 2nd International Symposium Quantum Theory and Symmetries, Krakow, 18-21 July, 2001
发表信息：
Proc. Second Int. Symp. on Quantum Theory and Symmetries, Krakow, Poland, July 18-21, 2001, Eds. E. Kapuscik and A. Horzela (World Scientific, Singapore, 2002) pp. 531-536
Two new types of coherent states associated with the $C_λ$-extended oscillator, where $C_λ$ is the cyclic group of order $λ$, are introduced. They satisfy a unity resolution relation in the $C_λ$-extended oscillator Fock space (or in some subspace thereof) and give rise to Bargmann representations of the latter, wherein the generators of the $C_λ$-extended oscillator algebra are realized as differential-operator-valued matrices.
Two new types of coherent states associated with the C_λ-extended oscillator, where C_λ is the cyclic group of order λ, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for λ=2, as well as the annihilation-operator coherent states of the C_λ-extended oscillator spectrum generating algebra for higher λvalues. The second ones, which are eigenstates of the C_λ-extended oscillator annihilation operator, extend to higher λvalues the paraboson coherent states, to which they reduce for λ=2. All these states satisfy a unity res…
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