sh(2/2) Superalgebra eigenstates and generalized supercoherent and supersqueezed states

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dc.creatorAlvarez-Moraga, Nibaldo
dc.creatorHussin, Veronique
dc.date2005-04-06
dc.date.accessioned2026-07-07T04:32:00Z
dc.date.available2026-07-07T04:32:00Z
dc.descriptionThe superalgebra eigenstates (SAES) concept is introduced and then applied to find the 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 $osp(2/2) \sdir sh(2/2)$ 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 superHermitian and $η$--pseudo--superHermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.
dc.description42 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0504018
dc.identifierhttp://arxiv.org/abs/math-ph/0504018
dc.identifierInter. J. Theor. Phys. Vol. 43, N. 1 (2004) 179-218
dc.identifierdoi:10.1023/B:IJTP.0000028859.11739.79
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58028
dc.subjectMathematical Physics
dc.titlesh(2/2) Superalgebra eigenstates and generalized supercoherent and supersqueezed states
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