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  • Books  (198)
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  • 11
    Electronic Resource
    Electronic Resource
    A dynamical formalism of singular Lagrangian system with higher derivatives (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1122-1132 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The singular Lagrangian system with higher derivatives is analyzed with the aid of the Ostrogradski transformation and the Dirac formalism. The formulation of canonical theory is developed so that the equivalence between the Lagrange formalism and the Hamilton one is maintained. As a practical example, the acceleration-dependent potentials appearing in the Lagrangian of two-point particles interacting gravitationally are dealt with and the equivalence between the two Hamiltonians that follow from the two Lagrangians which are related by the coordinate transformations is shown. It is also shown, when the constraints are all first class, that a consistent generator of gauge transformation is constructed. Typical examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528331
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  • 12
    Electronic Resource
    Electronic Resource
    Partial waves for the linearized Yang–Mills equation about a monopole background (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1150-1157 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The properties of the monopole-vector spherical harmonics that are needed to transform covariant differential equations on charged vector fields in the presence of a monopole into purely radial ones are computed. This further extends the work of Wu and Yang [Nucl. Phys. B 107, 365 (1976)]. As an application, the complete set of partial waves of SU(2) Yang–Mills fluctuations about the U(1) monopole configuration are explicitly computed. They are generated from the scalar solutions to the covariant Laplacian by the covariant operators D and r×D, in analogy with the uncharged case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528334
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  • 13
    Electronic Resource
    Electronic Resource
    R structures, Yang–Baxter equations, and related involution theorems (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1140-1149 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: There are several ways to construct functions in involution on a Lie bi-algebra, a Lie algebra equipped with a second Lie bracket. For the solvable systems associated to the Casimir functions a second Hamiltonian formulation can be constructed and a class of bi-Hamiltonian Korteweg–de Vries-like evolution equations with explicit space dependence is derived. Translating the Casimir functions with the flow of a special vector field yields another set of functions in involution. Lenard relations are found for the corresponding Hamiltonian systems. Finally, solutions of the classical Yang–Baxter equation lead to an analog of compatible Hamiltonian pairs. The invariants of the resulting hereditary operators are in involution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528333
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  • 14
    Electronic Resource
    Electronic Resource
    Expressions for the zeta-function regularized Casimir energy (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1133-1139 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The expansion of the Casimir energy for a scalar field with mass m, in a space where one dimension has been compactified into a circle of length a, leads to a double-infinite series that can be regularized by analytic continuation in the space dimension. The dimensionally regularized sum is then expressed as a power series in am by means of zeta-function expansions. The two possibilities of odd and even space dimensions are distinguished. In the odd space dimension we give a power expansion for small am, in addition to the asymptotic behavior. For the even space dimension, an expansion valid for any value of am is obtained. The contribution of higher-order terms is studied and, for the three-dimensional space, results for different values of the compactification length are shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528332
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  • 15
    Electronic Resource
    Electronic Resource
    Ordered exponentials and differential equations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1161-1163 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An independent and elementary method of guessing the leading form of certain SU(2) and SU(3) ordered exponentials in the strong-coupling limit of rapidly fluctuating input is presented. For SU(N), with N≥3, the method is not unambiguous, but it can be used to check previous estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528336
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  • 16
    Electronic Resource
    Electronic Resource
    Double-solution family of self-dual SU(2) gauge fields (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1158-1160 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The method of Witten [Phys. Rev. D 19, 718 (1979)] is extended to a double-complex form. Many new solutions of the self-dual SU(2) gauge fields are generated by the double-inverse scattering method, and the soliton solutions can form an infinite network.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528335
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  • 17
    Electronic Resource
    Electronic Resource
    On infinite-dimensional variational principles with constraints (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1171-1176 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Lagrange multiplier theorem is generalized for constrained functions on dual pairs of Banach spaces. Then a variational principle for dual pairs of Banach spaces is proven for the case when the constraint set is given by a symmetry and it is generalized to Banach manifolds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528338
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  • 18
    Electronic Resource
    Electronic Resource
    Existence of infinitely many zero-energy states in a model of supersymmetric quantum mechanics (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1164-1170 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The general framework of the N=2 Wess–Zumino holomorphic supersymmetric quantum mechanics with polynomial superpotentials is extended to the case of nonpolynomial superpotentials V(z) (z∈C) in a mathematically rigorous way. It is also proved that there exist no fermionic zero-energy states. Under some conditions for V, the operator domain of the supercharges and the supersymmetric Hamiltonian are identified. As an example, the model with V(z)=λeαz (λ∈C(large-closed-square){0}, α〉0) is analyzed in view of index theory. The following remarkable result is proved: There exist infinitely many bosonic zero-energy states which are localized in the momentum space dual to the Im z direction. The results are applied to two models in atomic and nuclear physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528337
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  • 19
    Electronic Resource
    Electronic Resource
    Conditions for runaway phenomena in the kinetic theory of particle swarms (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1177-1186 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The velocity distribution of a spatially uniform diluted guest population of charged particles moving within a host medium under the influence of a D. C. electric field is studied. A simplified one-dimensional Boltzmann model of the Kac type is adopted. Necessary conditions and sufficient conditions are established for the existence, uniqueness, and attractivity of a stationary non-negative distribution corresponding to a specified concentration level. Conditions for the onset of the runaway process are established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528339
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  • 20
    Electronic Resource
    Electronic Resource
    Construction of indecomposable representations of inhomogeneous Lie groups (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 965-969 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Simple methods of construction of indecomposable representations of inhomogeneous Lie groups are considered and applied to the Poincaré group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528341
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