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  • 1
    Electronic Resource
    Electronic Resource
    Boson–fermion and baryon mapping: Construction of collective subspaces. III. Application of the baryon mapping to many-baryon states (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3463-3467 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The theory developed in Paper I of this series is applied to the general case of a system consisting of colorfree quark triplets, whose quantum numbers are chosen as collective trifermion indices. The appropriate mapping technique to be used here is the baryon mapping. It is demonstrated that the original multiquark states can be exactly represented by states of colorfree ideal baryons. Besides, collective extended images are derived for a class of fermionic operators leaving the collective fermion space invariant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529894
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  • 2
    Electronic Resource
    Electronic Resource
    Gravitational equations in space-time with torsion (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3509-3520 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Various representations of equations of gravitational theories in space-time with torsion are considered. Special attention is paid to the case of quadratic Poincaré gauge theory of gravity. Advantages of each representation are discussed. The complete algorithm for calculation of gravitational equations in the framework of the most efficient formalism of spinor-valued exterior forms is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529902
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  • 3
    Electronic Resource
    Electronic Resource
    The Barut–Girardello coherent states (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 114-121 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the completeness problem of the SL(2,R) coherent states proposed by Barut and Girardello leads to a moment problem, not a Mellin transform. This moment problem, which also appears in the theory of para-Bose oscillators, has been solved following the Sharma–Mehta–Mukunda–Sudarshan solution of the problem. The matrix element of finite transformation in the coherent state basis is shown to satisfy a "quasiorthogonality'' condition analogous to the orthogonality condition of the matrix element in the canonical basis. Finally, the Barut–Girardello "Hilbert space of entire analytic functions of growth (1,1)'' turns out to be only a subspace of Bargmann's well-known Hilbert space of analytic functions. This subspace, which has been called "the reduced Bargmann space'' in a previous paper, is an invariant subspace of SL(2,R). With this identification the generators of the group in this realization turn out to be the well-known boson operators of Holman and Biedenharn.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529951
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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    On the evaluation of the U(3) content of the matrix elements of one- and two-body operators (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1550-1565 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An expression for the U(3) content of the matrix elements of one- and two-body operators in Elliott's basis is obtained. Three alternative ways of evaluating this content with increasing performance in computing time are presented. All of them allow an exact representation of that content in terms of integers, avoiding rounding errors in the computer codes. The role of dual bases in dealing with nonorthogonal bases is also clarified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529680
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  • 6
    Electronic Resource
    Electronic Resource
    Matrix elements and Wigner coefficients for Uq[gl(n)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1008-1022 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this series of papers the fundamental Wigner coefficients and the matrix elements of the generators for the quantum group Uq[gl(n)] are derived. The Uq[gl(n)]:Uq[gl(n−1)] reduced Wigner coefficients and reduced matrix elements are determined algebraically as eigenvalues of certain Uq[gl(n−1)] invariants in the quantum group Uq[gl(n)]. The matrix elements of the elementary quantum group generators, in the Gel'fand–Tsetlin basis, are derived below, while all fundamental Wigner coefficients are derived in the second paper of the series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529986
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  • 7
    Electronic Resource
    Electronic Resource
    Reduced Wigner coefficients for Uq[gl(n)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1023-1031 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This is the second paper in a series concerned with the Racah–Wigner calculus for the quantum group Uq[gl(n)]. In this approach all reduced Wigner coefficients are determined algebraically by the eigenvalues of certain generalized Casimir invariants. Here the method is applied to evaluate all fundamental Wigner coefficients and reduced Wigner coefficients for Uq[gl(n)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529764
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  • 8
    Electronic Resource
    Electronic Resource
    The initial value problem for a class of general relativistic fluid bodies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1047-1053 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A body or collection of bodies made of perfect fluid can be described in general relativity by a solution of the Einstein–Euler system where the mass density has spatially compact support. It is shown that for certain equations of state there exists a wide class of solutions of this type corresponding to appropriate initial data given on a spacelike hypersurface. This class is not constrained by any symmetry requirements. The key element of the proof is to write the equations as a symmetric hyperbolic system which is regular both for nonvanishing density and in vacuum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529766
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  • 9
    Electronic Resource
    Electronic Resource
    A superversion of quasifree second quantization. I. Charged particles (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1032-1046 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A formalism comprising and extending quasifree second quantization of charged bosons and fermions is presented. The second quantization of one-particle observables leads to current superalgebras, and a super-Schwinger term shows up. Anticommuting parameters are introduced in order to construct super-Bogoliubov transformations mixing bosons and fermions. As an application, representations of Lie superalgebras are given which are semidirect products of extensions of affine Kac–Moody algebras and the Virasoro algebra, and of the super-Virasoro algebra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529765
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  • 10
    Electronic Resource
    Electronic Resource
    Head-on collision of gravitational plane waves with noncollinear polarization: A new class of analytic models (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1054-1064 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new four-parameter class of exact solutions of Einstein's field equations is obtained, using the inverse scattering method of Belinsky and Zakharov. Its members represent the head-on collision of a variably polarized gravitational plane wave with one having constant polarization and, in general, different profile, or with an infinitely thin shell of null dust. In some of these models no curvature singularity develops along the future boundary of the region of interaction. In certain cases the singularity avoidance is the direct result of the noncollinear polarization of the waves involved in the collision.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529767
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