sh(2/2) Superalgebra Eigenstates and Generalized Supercoherent and Supersqueezed States

Authors: Alvarez-Moraga N.¹; Hussin V.²

Source: International Journal of Theoretical Physics, Volume 43, Number 1, January 2004 , pp. 179-218(40)

Publisher: Springer

Abstract:

The superalgebra eigenstates (SAES) concept is introduced and then applied to find SAES associated to the sh(2/2) superalgebra, also known as Heisenberg–Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the sh(2/2) SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the osp(2/2)&Eth; sh(2/2) superalgebra, where osp(2/2) denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg–Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the super-Hermitian and -pseudo-super-Hermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.

Keywords: superalgebra eigenstates; supercoherent; supersqueezed; Grassmann variables

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:IJTP.0000028859.11739.79

Affiliations: 1: Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada. Départment de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada 2: Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada. Départment de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada;, Email: hussin@dms.umontreal.ca

Publication date: 2004-01-01

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