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  • Articles  (15,427)
  • 1990-1994  (15,427)
  • 1993  (15,427)
  • Mathematics  (15,427)
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  • 1990-1994  (15,427)
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  • 1
    Electronic Resource
    Electronic Resource
    The pseudodifferential operator square root of the Klein–Gordon equation (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3918-3932 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A nonlocal square root of the Klein–Gordon equation is proposed. This nonlocal equation is a special relativistic equation for a scalar field of first order in the time derivative. Its space derivative part is described by a pseudodifferential operator. The usual quantum mechanical formalism can be set up. The nonrelativistic limit and the classical limit in the form of plane wave solutions and the Ehrenfest theorem are correctly included. The nonlocality of the wave equation does not disturb the light cone structure, and the relativity principle of special relativity is fulfilled. Uniqueness and existence of solutions of the Cauchy problem for this equation can be proved. The second quantized version of this theory turns out to be macrocausal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530015
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  • 2
    Electronic Resource
    Electronic Resource
    Analytic solution of the Bardeen–Cooper–Schrieffer gap equation in one, two, and three dimensions (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3980-3985 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Analytic expressions for the Bardeen–Cooper–Schrieffer (BCS) gap of a many-electron system with the BCS model interaction are obtained in one, two, and three dimensions in the weak coupling limit, but for arbitrary interaction width ν≡(h-dash-bar)ωD/EF, 0〈ν〈∞. Here (h-dash-bar)ωD is the maximum energy of a force-mediating boson, and EF is the Fermi energy (which is fixed by the electronic density). Our results address both phononic (ν(very-much-less-than)1) as well as nonphononic (e.g., exciton, magnon, plasmon, etc.) pairing mechanisms where the mediating boson energies are not small compared with EF, provided weak electron–boson coupling prevails. The essential singularity in coupling, sometimes erroneously attributed to the two-dimensional character of the BCS model interaction with ν(very-much-less-than)1, is shown to appear in one, two, and three dimensions before the limit ν→0 is taken.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530018
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  • 3
    Electronic Resource
    Electronic Resource
    Geometrization of classical mechanics (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4000-4006 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper, it is shown that the symplectic description of the Hamiltonian mechanics contains a gauge structure, where the symplectic form acts as connection form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530020
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  • 4
    Electronic Resource
    Electronic Resource
    Why do soliton equations come in hierarchies? (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4045-4049 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this article, an identity satisfied by the so-called recursion operator is derived. The identity generates by itself an infinite sequence of Lax pairs, thus ensuring the complete integrability of the corresponding hierarchy of nonlinear evolution equations. It is also shown that this identity yields the familiar property that the squares of eigenfunctions of the associated linear spectral problem satisfy the linearized version of the respective soliton equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530024
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  • 5
    Electronic Resource
    Electronic Resource
    Time-dependent Kaluza–Klein soliton solutions (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4070-4079 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Time-dependent generalizations of the standard static, spherically symmetric solutions of the empty Kaluza–Klein or (4+1) Einstein equations are considered herein. Such time-dependent solutions exist because Birkhoff's theorem does not hold in (4+1) gravity. The solutions depend on the time and radius but not the fifth or internal coordinate, and fall into four classes with distinct mathematical properties. Physically, some of our solutions represent a static 4D space–time with an oscillating or contracting extra dimension, which suggests their relevance to particle physics. Others represent an expanding 3D space with a contracting extra dimension, which suggests their relevance to cosmology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530027
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  • 6
    Electronic Resource
    Electronic Resource
    Equivalence between Lagrangian and Hamiltonian BRST formalisms (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3933-3953 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For a wide class of gauge invariant systems, the equivalence between Lagrangian and Hamiltonian BRST formalisms is proven.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530410
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  • 7
    Electronic Resource
    Electronic Resource
    Invariants and Lie algebraic solutions of Schrödinger equation (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3964-3979 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A representation of invariants in quantum mechanics for a general time-dependent Hamiltonian is provided. The main properties of these operators and their relevance for solving the Schrödinger equation are discussed in light of this representation. In particular, the well-known Lewis and Riesenfeld's method is shown to be recovered quite directly by the present approach. A detailed analysis is concerned with Hamiltonians which at each instant are elements of a finite dimensional Lie algebra. Exploiting the Wei and Norman's theory for such Hamiltonians, it is found that the evolution of a quantum system is always determined, in part or fully, by an invariant which belongs to the same algebra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530017
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  • 8
    Electronic Resource
    Electronic Resource
    Band representations and duals of the nonsymmorphic crystallographic plane groups pg and p4gm (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4112-4137 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Duals of the groups pg and p4gm are constructed. (1) The group pg has only one band representation (an elementary one) equivalent to the regular representation. There exists a quasiband representation close to it, of multiplicity two, which separates the branches of the band. Finite groups which approximate pg are discussed. (2) Two elementary band representations associated with the Wyckoff position b of the group p4gm are shown to be nonequivalent although they have the same decomposition in unirreps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530030
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  • 9
    Electronic Resource
    Electronic Resource
    The projective unitary irreducible representations of the Poincaré group in 1+2 dimensions (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4172-4189 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A complete analysis is given of the projective unitary irreducible representations of the Poincaré group in 1+2 dimensions applying the Mackey theorem and using an explicit formula for the universal covering group of the Lorentz group in 1+2 dimensions. Explicit formulas are given for all representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529994
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  • 10
    Electronic Resource
    Electronic Resource
    Deformations of Lie group and Lie algebra representations (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4251-4272 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A complete study of deformations of Lie group and Lie algebra representations, including differentiability and integrability results, is given. Adapted results are given in the semisimple case. A notion of induced deformations is introduced. Various examples are given, including deformations of indecomposable representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529998
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