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  • 1990-1994  (10)
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  • 1
    Electronic Resource
    Electronic Resource
    On pararelativistic quantum oscillators (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3387-3392 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Different choices of matrices characterizing p=2 parafermions are analyzed in connection with the description of relativistic spin-one particles through the Kemmer formulation. The free and interacting cases are considered and the relations between parasupersymmetry and Kemmer theory are enhanced as it is also the case between supersymmetry and Dirac theory. In that way the oscillatorlike context leads to the characterization of pararelativistic oscillators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529886
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  • 2
    Electronic Resource
    Electronic Resource
    Lie structures in parasupersymmetric quantum mechanics: II. The spin-orbit coupling supersymmetrization procedure (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1815-1821 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The spin-orbit coupling supersymmetrization procedure is considered in parasupersymmetric quantum mechanics describing oscillatorlike systems. The superposition of bosonic and parafermionic degrees of freedom is mainly studied in the cases of two and three spatial dimensions but the n-dimensional case is also determined. New Lie superalgebras and Lie parasuperalgebras are pointed out: They differ from those already obtained in connection with the standard procedure of supersymmetrization studied in Part I of this series [J. Beckers and N. Debergh, J. Math. Phys. (square, solid)(square, solid), (square, solid)(square, solid)(square, solid) (1991)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529246
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Lie structures in parasupersymmetric quantum mechanics: I. The standard supersymmetrization procedure (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1808-1814 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Parasupersymmetric quantum mechanics leads to the construction of new Lie structures that are called Lie parasuperalgebras. They are characterized by double commutation relations between even and odd generators and include as particular substructures the usual Lie superalgebras. Oscillatorlike systems in one spatial dimension are especially exploited in order to put such structures in evidence but n-dimensional extensions are easily determined. These developments in the standard supersymmetrization procedure will be considered first and the spin orbit coupling one will be considered in a subsequent article [J. Beckers and N. Debergh, J. Math. Phys. (square, solid)(square, solid), (square, solid)(square, solid)(square, solid) (1991)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529245
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  • 4
    Electronic Resource
    Electronic Resource
    On supersymmetric harmonic oscillators and the Green–Cusson Ansätze (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 3094-3100 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: New properties on parabosonic and parafermionic Cusson's realizations of the Green's Anzätze are first obtained. Then paraproperties are shown to have a specific interest for our real world, where bosons and fermions have to be superposed if Nature is supersymmetric, these results being obtained on supersymmetric harmonic oscillators. In particular, from the Green–Cusson Ansätze, we construct a class of supersymmetric Hamiltonians that are more general than the ones issued from standard or spin–orbit coupling considerations. We explicitly consider the simplest (previously unknown) super-Hamiltonian constructed from paraproperties in quantum mechanics and establish its invariance Lie superalgebra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529056
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  • 5
    Electronic Resource
    Electronic Resource
    Superposition formulas for nonlinear superequations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2528-2534 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Nonlinear superequations, for which the general solution can be expressed algebraically in terms of a finite number of particular solutions, are obtained. They are based on the orthosymplectic supergroup OSP(m,2n) and its action on a homogeneous superspace. Superposition formulas are discussed for the cases m=1, n arbitrary, and m=2, n=1. For OSP(2,2) the number of particular solutions needed to reconstruct the general solution depends on the dimension of the underlying Grassmann algebra, whereas for OSP(1,2n) it does not.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528997
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  • 6
    Electronic Resource
    Electronic Resource
    Adaptive Optics for Astronomy: Principles, Performance, and Applications (1993)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Astronomy and Astrophysics 31 (1993), S. 13-62 
    Details
    ISSN: 0066-4146
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.aa.31.090193.000305
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  • 7
    Electronic Resource
    Electronic Resource
    On a family of supersymmetrization procedures (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3378-3390 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Generalized expressions are proposed for the supercharges in N=2 supersymmetric quantum mechanics and their implications are analyzed mainly in the one-dimensional context. In fact, these generalizations are exploited in three typical examples admitting the largest numbers of symmetries, i.e., the harmonic oscillator, the hydrogen atom, and their superposition, the so-called "Calogero context,'' successively. Different matrix realizations are exploited in the harmonic oscillator case more particularly. The link between these considerations and quantum deformations must be insisted on, our deformation b parameter referring to a family of physically acceptable supersymmetrization procedures including, in particular, the standard one (when b→1) initially proposed by Witten.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530082
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  • 8
    Electronic Resource
    Electronic Resource
    On supersymmetries in nonrelativistic quantum mechanics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 152-160 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed out. The study of even supersymmetries is particularly enlightened through the already known symmetries of the corresponding Schrödinger equation. Three tables collect the even, odd, and total supersymmetries as well as the invariance (super)algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529954
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  • 9
    Electronic Resource
    Electronic Resource
    Parastatistics, supersymmetry and parasupercoherent states (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1513-1523 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Coherent states are constructed in p=2-parasupersymmetric quantum mechanics in connection with the two relative para-Bose and para-Fermi sets of trilinear structure relations. They are called parasupercoherent states. Parasupersymmetric operators [such as the Hamiltonian and (two) annihilation operators] are introduced and discussed. In particular, the parasuperspectrum is determined and compared with the recent results obtained by Rubakov and Spiridonov [Mod. Phys. Lett. A 3, 1337 (1988)]. The superalgebra contents subtended by osp(2/2) and osp(3/2) are analyzed and exploited in order to get constants of motion in both contexts through parallel properties on the supersymmetric harmonic oscillator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528694
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  • 10
    Electronic Resource
    Electronic Resource
    On partner potentials in parasupersymmetric quantum mechanics (1991)
    Springer
    The European physical journal 51 (1991), S. 519-524 
    Details
    ISSN: 1434-6052
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The constraint on the two superpotentials characterizing a parasuperhamiltonian is shown to be a Riccati equation which helps us for studying partner potentials. We point out that only three different types of parasuperspectra can appear. The simplest type admitting a unique non degenerate zero energy value can be associated with different models already discussed in other contexts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01548579
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