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arXiv:hep-ph/9604248 · Annals of Physics

Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

E. Celeghini, Salvatore DeMartino, S. Desiena, Mario Rasetti, Giuseppe Vitiello

Published Jul 1, 1995• 60 citations
arXivHTMLPDF
DOI
10.1006/aphy.1995.1055

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The Jacobi group the semidirect product of the Heisenberg group and the symplectic group [1–3] is an important object in quantum mechanics, geometric quantization, optics [4–6]. The Jacobi group is responsible for the squeezed states [7–12] in quantum optics [5], [6], [13], [14]. Some coherent state systems based on SiegelJacobi domains [15], [16] have been investigated in the framework of quantum mechanics, geometric quantization, dequantization, quantum optics, nuclear structure, and signal processing [17], [18], [19], [20][23]. We have attached in [20] Perelomov’s coherent states [24] to the Jacobi group G1∗= H1(R)nSU(1,1), based on the Siegel-Jacobi disk D1 =C×D1, where D1 = {z ∈ C||z| . ez ∈ H denotes the Perelomov coherent state vector indexed by the points z of the homogeneous manifold M = G/H , where H is compact subgroup of G. The generalized squeezed states of the type introduced in [22], [23], [25] are not new [8, 26, 27]. The paper is organized as follows. §2 collects the main notation concerning