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Bosonic and k-fermionic coherent states for a class of polynomial Weyl-Heisenberg algebras
Daoud M., Kibler M. R.
Journal of Physics A: Mathematical and Theoretical 45 (2012) 244036 - http://hal.in2p3.fr/in2p3-00634551
Physique/Physique Quantique
Mathématiques/Physique mathématique
Bosonic and k-fermionic coherent states for a class of polynomial Weyl-Heisenberg algebras
Mohammed Daoud ()1, Maurice R. Kibler ()1
1 :  IPNL - Institut de Physique Nucléaire de Lyon
http://www.ipnl.in2p3.fr/
CNRS : UMR5822 – IN2P3 – Université Claude Bernard - Lyon I
France
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 A(x), 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 su(1,1) algebra (for x > 0), the su(2) algebra (for x < 0) and the h(4) ordinary Weyl-Heisenberg algebra (for x = 0). For finite-dimensional representations of A(x) and A(x,s), where A(x,s) is a truncation of order s of A(x) 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 A(x) and for finite-dimensional representations of A(x) and A(x,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 A(x). In contrast, the construction of à la Barut-Girardello coherent states for finite-dimensional representations of A(x) and A(x,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 su(2), su(1,1) and the harmonic oscillator (in a truncated or not truncated form).

Articles dans des revues avec comité de lecture
2012
Journal of Physics A: Mathematical and Theoretical
Publisher Institute of Physics: Hybrid Open Access
ISSN 1751-8113 (eISSN : 1751-8121)
45
244036

03.65.Fd, 03.65.Ta, 02.20.Qs
25 pages
Perelomov coherent states – Barut-Girardello coherent states – generalized Weyl-Heisenberg algebra – su(2) algebra – su(1 – 1) algebra – harmonic oscillator algebra
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