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  • 1
    Electronic Resource
    Electronic Resource
    On generalized coherent states with maximal symmetry for the harmonic oscillator (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1732-1738 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Generalized coherent states for the one-dimensional harmonic oscillator with maximal symmetry, i.e., admitting the semidirect sum so(2,1) (D'Alembertian) h(2) as the largest invariance Lie algebra pointed out by Niederer are constructed. The normalization of such states as well as their completeness property are determined and discussed. They are also analyzed in the subcontexts of the so(2,1) algebra and of the Heisenberg h(2) algebra. General considerations on Heisenberg relations, on minimal dispersions, and on quantum mechanical entropies are presented in connection with the uncertainty principle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528261
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  • 2
    Electronic Resource
    Electronic Resource
    Nonlinear equations with superposition formulas and the exceptional group G2. I. Complex and real forms of g2 and their maximal subalgebras (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2217-2227 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In order to study nonlinear ordinary differential equations with superposition principles, related to the exceptional simple Lie group G2, the complex and real forms of its Lie algebra are examined and their maximal subalgebras are summarized. In particular the parabolic subalgebras of the noncompact real form gNC2(R) are determined. Explicit matrix realizations of the fundamental representation D(1,0) are used and studied in connection with invariant subspaces in a seven-dimensional (complex or real) vector space. The results are collected in three tables of specific interest for the study of nonlinear differential equations, which will be developed in Paper II of this series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526993
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  • 3
    Electronic Resource
    Electronic Resource
    On U(1)-gauge fields and their geometrical interpretation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 925-928 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Harnad–Shnider–Vinet study of symmetry properties on gauge fields in terms of invariant connections on principal fiber bundles is reviewed in the simple U(1)-gauge theory. It is extended to the case of invariant electromagnetic fields admitting nontrivial extensions of their symmetry groups. Some specific examples are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526548
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  • 4
    Electronic Resource
    Electronic Resource
    Nonlinear equations with superposition formulas and the exceptional group G2. II. Classification of the equations (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 520-529 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Nonlinear equations with superposition formulas are obtained, corresponding to the action of the complex and real forms of the exceptional Lie group G2 on the homogeneous spaces G2/H. The isotropy group of the origin H is taken as one of the maximal parabolic subgroups of G2, or as one of the maximal reductive subgroups, leaving some vector space V∈C7 (or V∈R7) invariant. The parabolic subgroups, as well as the simple subgroups SL(3,C), SU(3), SL(3,R) or SU(2,1) lead to equations with quadratic or quartic nonlinearities. The semisimple subgroups SL(2,C)⊗SL(2,C), SU(2)⊗SU(2), and SU(1,1)⊗SU(1,1) lead to equations with quadratic nonlinearities and additional nonlinear constraints on the independent variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527636
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  • 5
    Electronic Resource
    Electronic Resource
    On chains of orthosymplectic Lie superalgebras and the n-dimensional quantum harmonic oscillator (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1655-1661 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Triplets of embedded orthosymplectic Lie superalgebras are singled out and analyzed in terms of their respective even and odd root systems. The corresponding chains of embeddings are considered for arbitrary integers m and n (for both m≠n and m=n). It is shown that the second member inside each triplet is always in a one-to-one correspondence with the semidirect sum of the third member and the associated Heisenberg superalgebra that is characterized by the same entries m and n. For arbitrary m=n, invariance superalgebras of the n-dimensional harmonic oscillator are recovered and their one-to-one correspondence associated with a recent "character reversal'' phenomenon linking these invariance superstructures is rigorously explained. Specific and general cases as well as conclusions are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528250
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  • 6
    Electronic Resource
    Electronic Resource
    On the Heisenberg and orthosymplectic superalgebras of the harmonic oscillator (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1705-1711 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The new invariance superalgebra osp(2,2n)(+sh(2,2n) for an n-dimensional quantum harmonic oscillator is proposed, and the corresponding supersymmetric Hamiltonian is constructed. This superalgebra is related to the structure osp(3,2n) recently studied by Englefield [J. Phys. A 21, 1309 (1988)]. By interchanging the even and odd characters of the fundamental generators belonging to the Heisenberg superalgebra sh(2,2n), the connection between both structures is established and its consequences exploited. The specific cases n=1,2,3 are discussed and compared with recent contributions. Some general conclusions are also summarized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527867
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  • 7
    Electronic Resource
    Electronic Resource
    Surgical treatment of aspergillus spondylodiscitis (2000)
    Springer
    European spine journal 9 (2000), S. 75-79 
    Details
    ISSN: 1432-0932
    Keywords: Key words Aspergillosis ; Spondylodiscitis ; Debridement ; Spinal fusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Four cases of aspergillus spondylodiscitis were treated with operative debridement and fusion. In this rarely encountered mycotic infection of the spine in immunocompromised patients rapid destruction of the intervertebral disc and vertebral bodies can occur. In advanced cases antimycotic drug therapy is thought to be ineffective and a forcing indication for surgery exists when the destruction is progressive and spinal cord compression is imminent or manifest. Spinal instrumentation can be of help in maintaining or restoring spinal stability and maintaining spinal alignment. ¶In our four patients the aspergillus spondylodiscitis was successfully eradicated and fusion achieved. In two of three patients with a neurologic deficit, this deficit disappeared. Two patients died within 6 months after the operative treatment, due to complications related to the underlying illness. One patient was left with a subtotal paraplegia.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s005860050014
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  • 8
    Electronic Resource
    Electronic Resource
    Oscillator-Like Hamiltonians and Squeezing (2000)
    Springer
    International journal of theoretical physics 39 (2000), S. 1515-1527 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Generalizing a recent proposal leading to one-parameter families of Hamiltoniansand to new sets of squeezed states, we construct larger classes of physicallyadmissible Hamiltonians permitting new developments in squeezing. We alsodiscuss coherence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1003684011477
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  • 9
    Electronic Resource
    Electronic Resource
    Nonlinear differential equations and lie superalgebras (1987)
    Springer
    Letters in mathematical physics 13 (1987), S. 113-120 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Nous montrons comment la théorie des équations différentielles ordinaires non-linéaires admettant des lois de superposition peut être généralisée au cas de ‘super-équations’ contenant des variables de Grassmann anticommutantes. Comme exemple les équations basées sur la super-algèbre osp(1, 2) sont analysées en détail. Nous obtenons des super-équations de Riccati et leurs formules de superposition sont mises en évidence.
    Notes: Abstract It is shown how the theory of nonlinear ordinary differential equations with superposition formulas can be generalized to the case of ‘superequations’ involving anticommuting Grassmann variables. As an example, equations based on the osp(1, 2) superalgebra are analyzed in detail. They turn out to be ‘super-Riccati’ equations and a ‘super-superposition’ formula is obtained for their solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00955198
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  • 10
    Electronic Resource
    Electronic Resource
    Complex parabolic subgroups of G 2 and nonlinear differential equations (1986)
    Springer
    Letters in mathematical physics 11 (1986), S. 81-86 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Nonlinear ordinary differential equations with superposition formulas corresponding to the exceptional Lie group G 2ℂ and its two maximal (complex) parabolic subgroups are determined. The G 2-invariance of a third-order skewsymmetric tensor is exploited. The obtained ODEs have polynomial nonlinearities of order 2 in one case and of order 4 in the other.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00417468
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