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- W2004010937 abstract "Coherent states corresponding to different series of representations of the group SL(2,R) are introduced. The infinite sums of such coherent states may lead to automorphic forms on a discontinuous subgroup Γs ⊂ SL(2,R) if certain conditions are fulfilled. The obtained forms may be considered as “fixed” states, and the group Γs as the corresponding stationary group. Starting with this composite “fixed” state, “composite” coherent states are defined in the usual manner. Mellin transforms of the coherent states, interesting from the physical point of view are examined. As a first example, it is shown that, under certain circumstances, the Mellin transform of a first kind coherent state is a Veneziano amplitudelike function. A second example starts with a two-dimensional theta wave packet (i.e. a two-dimensional free wave packet with Gaussian structure in the momentum space). The Mellin transform is an Epstein ζ-function; if the uncertainties of the momenta are satisfying the relation Δk21Δk22 = (Δk1Δk2)2, the Mellin transform is an Eisenstein series. The Maass series are obtained as Mellin transforms of an adequately redefined theta wave packet." @default.
- W2004010937 created "2016-06-24" @default.
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- W2004010937 date "1977-08-01" @default.
- W2004010937 modified "2023-10-18" @default.
- W2004010937 title "Coherent states on the group SL(2, R). series of coherent states and automorphic forms; Mellin transforms" @default.
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- W2004010937 doi "https://doi.org/10.1016/0034-4877(77)90049-0" @default.
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