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Partially coherent states of the real symplectic group

par Deenen, Jacques ;Quesne, Christiane
Référence Journal of mathematical physics, 25, 8, page (2354-2366)
Publication Publié, 1984

Article révisé par les pairs

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Résumé :

In the present paper, we introduce partially coherent states for the positive discrete series irreducible representations <λd + n/2,...,λ1 + n/2> of Sp(2d,R), encountered in physical applications. These states are characterized by both continuous and discrete labels. The latter specify the row of the irreducible representation [λ1λ2⋯λd] of the maximal compact subgroup U(d), while the former parametrize an element of the factor space Sp(2d,R)/H, where H is the Sp(2d,R) subgroup leaving the [λ1λ2⋯λd] representation space invariant. We consider three classes of partially coherent states, respectively, generalizing the Perelomov and Barut-Girardello coherent states, as well as some recently introduced intermediate coherent states. We prove that each family of partially coherent states forms an overcomplete set in the representation space of <λd + n/2,..., λ1 + n/2>, and study its generating function properties. We show that it leads to a representation of the Sp(2d,R) generators in the form of differential operator matrices. Finally, we relate the latter to a boson representation, namely a generalized Dyson representation in the cases of Perelomov and Barut-Girardello partially coherent states, and a generalized Holstein-Primakoff representation in that of the intermediate partially coherent states. © 1984 American Institute of Physics.