Generalized Coherent States for Polynomial Weyl-Heisenberg AlgebrasReport as inadecuate

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1 IPNL - Institut de Physique Nucléaire de Lyon

Abstract : It is the aim of this paper to show how to construct Perelomov and Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This algebra depends on r parameters. For some special values of the parameter corresponding to r = 1, the algebra covers the cases of the su1,1 algebra, the su2 algebra and the ordinary Weyl-Heisenberg or oscillator algebra. For r arbitrary, the generalized Weyl-Heisenberg algebra admits finite or infinite-dimensional representations depending on the values of the parameters. Coherent states of the Perelomov type are derived in finite and infinite dimensions through a Fock-Bargmann approach based on the use of complex variables. The same approach is applied for deriving coherent states of the Barut-Girardello type in infinite dimension. In contrast, the construction of Barut-Girardello coherent states in finite dimension can be achieved solely at the price to replace complex variables by generalized Grassmann variables. Finally, some preliminary developments are given for the study of Bargmann functions associated with some of the coherent states obtained in this work.

Keywords : polynomial Weyl-Heisenberg algebra su1 1 su2 oscillator algebra generalized Perelomov coherent states generalized Barut-Girardello coherent states Bargmann functions

Author: Maurice Robert Kibler - Mohammed Daoud -



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