Bosonic and k-fermionic coherent states for a class of polynomial Weyl-Heisenberg algebrasReport as inadecuate




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1 IPNL - Institut de Physique Nucléaire de Lyon

Abstract : The aim of this article is to construct à la Perelomov and à la Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This generalized Weyl-Heisenberg algebra, noted Ax, depends on r real parameters and is an extension of the one-parameter algebra introduced in Daoud M and Kibler MR 2010 J. Phys. A: Math. Theor. 43 115303 which covers the cases of the su1,1 algebra for x > 0, the su2 algebra for x < 0 and the h4 ordinary Weyl-Heisenberg algebra for x = 0. For finite-dimensional representations of Ax and Ax,s, where Ax,s is a truncation of order s of Ax in the sense of Pegg-Barnett, a connection is established with k-fermionic algebras or quon algebras. This connection makes it possible to use generalized Grassmann variables for constructing certain coherent states. Coherent states of the Perelomov type are derived for infinite-dimensional representations of Ax and for finite-dimensional representations of Ax and Ax,s through a Fock-Bargmann analytical approach based on the use of complex or bosonic variables. The same approach is applied for deriving coherent states of the Barut-Girardello type in the case of infinite-dimensional representations of Ax. In contrast, the construction of à la Barut-Girardello coherent states for finite-dimensional representations of Ax and Ax,s can be achieved solely at the price to replace complex variables by generalized Grassmann or k-fermionic variables. Some of the results are applied to su2, su1,1 and the harmonic oscillator in a truncated or not truncated form.

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





Author: Mohammed Daoud - Maurice Kibler -

Source: https://hal.archives-ouvertes.fr/



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