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  • Articles  (32,818)
  • 1995-1999  (32,818)
  • Mathematics  (32,818)
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  • Articles  (32,818)
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  • 1
    Electronic Resource
    Electronic Resource
    An estimation theoretical characterization of coherent states (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4227-4239 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We introduce a class of quantum pure state models called the coherent models. A coherent model is an even-dimensional manifold of pure states whose tangent space is characterized by a symplectic structure. In a rigorous framework of noncommutative statistics, it is shown that a coherent model inherits and expands the original spirit of the minimum uncertainty property of coherent states. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532962
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  • 2
    Electronic Resource
    Electronic Resource
    Partially solvable quantum many-body problems in D-dimensional space (D=1,2,3,...) (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4208-4226 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple technique employed almost three decades ago to manufacture partially solvable quantum many-body problems is revisited. [A quantum problem is "partially solvable" if (only) some of its eigenvalues and eigenfunctions can be exhibited]. The models thereby generated are characterized by Hamiltonians of normal form, i.e., standard kinetic plus momentum-independent potential energy; in most cases the latter features three-body, in addition to two-body and one-body, interactions. The setting refers to D-dimensional space; the examples focus on D=1, D=2, and D≥2, and include generalizations of, and additional results on, cases recently discussed in the literature, as well as new models. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532961
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  • 3
    Electronic Resource
    Electronic Resource
    Point and line boundaries in scalar Casimir theory (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4185-4207 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple image-charge construction enables one to insert point or line boundaries (or planar or hyperplanar boundaries when sufficiently many spatial dimensions are available) at or into the central point, line, plane etc., of a great range of spatial backgrounds in quantum field theory which have appropriate symmetry. This nontrivial construction (which provides among other things the exact vacuum stress tensor Tμν of the quantum field if Tμν can be computed for the original background prior to point, line,..., insertion) works if all directions xi perpendicular to the inserted object are symmetric under xi→−xi. In other respects the symmetric spatial background can be quite arbitrary. While the inserted object experiences (by symmetry) no net Casimir force from the background, it does exert Casimir forces throughout this background which were originally not present. In addition to general theory, detailed examples are given (which include exact field Tμν's and exact Casimir force densities) for arbitrary spatial dimension. First: point and line boundaries in otherwise empty space; then a planar boundary with a semi-infinite line extending from one side; finally, parallel planar boundaries with a point boundary halfway between them. Only scalar quantum fields are analyzed here; however the extension to the electromagnetic Casimir effect is discussed qualitatively. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532960
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  • 4
    Electronic Resource
    Electronic Resource
    Exact solutions of Dirac equation for neutrinos in presence of external fields (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4240-4254 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Exact solutions of the Dirac equation in a chiral representation for neutrinos in the presence of external stresses are investigated in terms of special functions, using the algebraic method of the separation of variables in Cartesian, cylindrical, and spherical coordinates. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532963
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  • 5
    Electronic Resource
    Electronic Resource
    Exactly solvable models of δ′-sphere interactions in nonrelativistic quantum mechanics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4255-4273 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We introduce and perform a systematic study of a new exactly solvable model of sphere interactions in quantum mechanics : the δ′ interaction, formally given by −Δ+αδ′(|x|−R), x∈R3, R〉0, α∈R. We also consider the cases of a δ′ plus a Coulomb interaction and finitely many δ′-sphere interactions with support on concentric spheres. For all these models, we provide basic properties and discuss the stationary scattering theory. We also briefly discuss the δ′-sphere interaction of the second type. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532964
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  • 6
    Electronic Resource
    Electronic Resource
    On a purported local extension of the quantum formalism (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4290-4295 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is widely believed that Bell has proved there can be no consistent local extension of the quantum formalism. Against this, Angelidis has presented a hidden variable theory which, he claims, makes precisely the same predictions as the quantum formalism and which also satisfies locality. In this note, we argue that Angelidis' theory does not live up to its inventor's claims. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532966
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  • 7
    Electronic Resource
    Electronic Resource
    Degeneracy and para-supersymmetry of Dirac Hamiltonian in (2+1)-space–time (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4274-4289 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quantum mechanics of a spin 〈fraction SHAPE="CASE"〉12 particle on a locally spatial constant curvature part of a (2+1)-space–time in the presence of a constant magnetic field of a magnetic monopole has been investigated. It has been shown that these two-dimensional Hamiltonians have the degeneracy group of SL(2,c), and para-supersymmetry of arbitrary order or shape invariance. Using this symmetry we have obtained its spectrum algebraically. The Dirac's quantization condition has been obtained from the representation theory. Also, it is shown that the presence of angular deficit suppresses both the degeneracy and shape invariance. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532965
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  • 8
    Electronic Resource
    Electronic Resource
    On one generalization for the projection matrices method in the S-matrix factorization problem (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4296-4302 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A boundary value problem for a 2×2 S-matrix is solved by the method of projection matrices. The S-matrix is assumed to be diagnoalized by orthogonal matrix U(k2)=Ω(k2)/det Ω(k2), where matrix elements of Ω(k2) are polynomials. The equation det Ω(k2)=0 has roots of any order. The example is considered for the roots with order 2. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532967
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  • 9
    Electronic Resource
    Electronic Resource
    Classical mechanics and geometric quantization on an infinite dimensional disc and Grassmannian (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4303-4324 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss the classical mechanics on the Grassmannian and the disc modeled on the ideal L(2,∞). We apply methods of geometric quantization to these systems. Their relation to a flat symplectic space is also discussed. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532968
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  • 10
    Electronic Resource
    Electronic Resource
    Gauge theory of w symmetry (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4325-4330 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The w∞ algebra is a higher-spin extension of the Virasoro algebra. In this paper, we construct the gauge theory of w symmetry in terms of its representations. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532969
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