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  • Articles  (17,718)
  • 2015-2019
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  • Books  (35)
  • Articles  (17,718)
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  • 2015-2019
  • 2005-2009
  • 1995-1999
  • 1985-1989  (17,753)
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  • 101
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    Infinitesimal null isotropy and Robertson–Walker metrics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 407-410 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The concept of infinitesimal null isotropy is defined for a Lorentz manifold, in terms of null sectional curvature (as defined by Harris). It is shown that infinitesimal null isotropy is equivalent to infinitesimal spatial isotropy (as defined by Karcher), and that a null-isotropic space for which null sectional curvature is infinitesimally spatially constant must have a Robertson–Walker metric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526623
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  • 102
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    Some properties of hyperspherical harmonics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 396-403 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general formula is given for the canonical decomposition of a homogeneous polynomial of order λ in m variables into a sum of harmonic polynomials. This formula, which involves successive applications of the generalized Laplace operator, is proved in the Appendix. It is shown that the group-theoretical method for constructing irreducible Cartesian tensors follows from the general formula for canonical decomposition. The relationship between harmonic polynomials and hyperspherical harmonics is discussed, and an addition theorem for hyperspherical harmonics is derived. An expansion of a many-dimensional plane wave in terms of Gegenbauer polynomials and Bessel functions is derived and used to construct bicenter expansions of arbitrary functions in many-dimensional spaces. Finally, a formula is derived for the 3λ coefficients of hyperspherical harmonics. These coefficients give the values of integrals involving the products of three harmonics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526621
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  • 103
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    The anti-self-dual Coulomb field in Minkowski space-time (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 428-430 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The twistor encoding of the anti-self-dual Coulomb field is given in terms of the space-time connections pulled back to I+ and to I−. This description differs considerably from that of the twistor encoding of transverse or radiation fields, which have been the only fields studied in this fashion to date. A twisted structure results on I+ and a topologically incomputable one on I− and these are identified modulo the null lines intersecting the source world-line.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526626
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  • 104
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    A twistor encoding of Lienard–Wiechert fields in Minkowski space-time (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 431-433 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The twistor encoding of the anti-self-dual Lienard–Wiechert field on Minkowski space-time yields a considerably richer structure than that of the Coulomb field encoding due to the presence of a nonzero radiation field. The combination of advanced and retarded transverse fields together with the longitudinal field and the individual aspects of these fields provides this structure. Higher-order longitudinal moments can be incorporated so that general longitudinal fields can be given a twistor description.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526627
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  • 105
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    Three-dimensional inverse scattering: High-frequency analysis of Newton's Marchenko equation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 436-439 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We obtain a high-frequency asymptotic expansion of Newton's Marchenko equation for three-dimensional inverse scattering. We find that the inhomogeneous term contains the same high-frequency information as does the Born approximation. We show that recovery of the potential via Newton's Marchenko equation plus the "miracle'' depends on low-frequency information.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526629
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  • 106
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    Semiclassical statistical mechanics of two-dimensional fluid mixture of hard disks (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 495-504 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: High-temperature expansions for the density-independent part of the radial distribution function and the first-order density correction to it are obtained for a two-dimensional binary mixture of hard disks. The "excess'' quantum corrections to the second and third virial coefficients and excess free energy are also discussed. It is found that the "excess'' quantum effect depends on the concentration and the diameter radio.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526637
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  • 107
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    Exact temporal evolution for some nonlinear diffusion processes (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 522-527 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Exact solutions to Fokker–Planck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526639
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  • 108
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    Some static solutions in the general scalar-tensor theory (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 532-535 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Exact solutions are found for the static gravitational fields for a matter-free space in the general scalar-tensor theory of Nordtvedt–Barker–Schwinger. The singular behavior of some of the invariants has also been discussed for the solutions in Barker and Schwinger theories.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526641
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  • 109
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    Fermionic couplings in Kaluza–Klein theories (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 536-541 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The totally symmetric and totally antisymmetric direct couplings of fermions in d-dimensional space are investigated. Explicit forms are given for d〈11. A different way of handling the d-dimensional Dirac algebra is also described.
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    URL: http://dx.doi.org/10.1063/1.526642
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  • 110
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    A vector model for electroweak interactions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 542-550 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we present a vector model for the electroweak interactions. The Cartan map gives an isomorphism between Dirac bispinors and an isotropic class of Yang–Mills vector fields. The isotropic Yang–Mills vector fields Fk =Ek +iHk with k=1,2,3, satisfy the condition that the matrix of scalar invariants (Fj ⋅Fk) equals a scalar multiple of the identity matrix. We show that all the bispinor observables commute with the Cartan isomorphism, including all gauge transformations, as well as Lorentz transformations. We derive the Yang–Mills equivalent Dirac equation. As a consequence of the vector model, we obtain a new Lagrangian for electroweak interactions, which is an alternative to the Weinberg–Salam Lagrangian. Moreover, we show that the vector model predicts that the Weinberg angle θw satisfies sin2 θw =0.25, which is close to the measured value of sin2 θw =0.23. The vector model accommodates all the lepton and quark flavors. Furthermore, it predicts the conservation of baryon number and lepton number, as well as electric charge in electroweak interactions. The vector model also gives a new interpretation to antiparticles. In the vector model, an antiparticle is characterized by its opposite baryon number, lepton number, and electric charge; yet both particles and antiparticles propagate forward in time with positive energies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526588
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  • 111
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    Morphisms of crystallographic groups: Kernels and images (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 219-228 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The crystallographic groups play an important role in solid state physics, where their representations are of particular interest. In this paper we classify the kernels of all possible representations by deriving necessary and sufficient conditions for a subgroup H of a crystallographic group G to be invariant. The structure of G/H is also discussed. A list of the one- and two-dimensional invariant subgroups of the two-dimensional crystallographic groups is appended as Table I; it includes the structural features of these subgroups needed for determining their settings, relative to the parent groups, and identifies the corresponding images. Table II is a list of the commutator subgroups of the two-dimensional groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526651
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  • 112
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    Exact calculation of the lineshape and the scattering operator for a model of a two-level atom interacting with a continuous spectrum of radiation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 556-565 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we calculate exactly the lineshape for a model of an excited two-level atom in interaction with a continuous spectrum of radiation for the problem of spontaneous emission. Specifically, for the case of a d=1 radiation field, we use the exact results reported in our earlier work [J. Math. Phys. 14, 414, 423 (1973)] for the probability ρ(τ) of the atom's being in the excited state at time τ to obtain an analytic expression for the lineshape of the emitted radiation (i.e., the photon). We also calculate the lineshape using two Wigner–Weisskopf style approximations and the results, for a given choice of coupling function, are compared numerically with the profile generated using the exact solution. These comparisons show convincingly the success with which these two approximations can be expected to reproduce the qualitative and quantitative features of the exact lineshape for values of the coupling constant α ranging between 0.01 and 0.3. Finally, we calculate explicitly the scattering operator corresponding to the above spontaneous emission problem and work out exactly the probability of forward and backward scattering of a photon by the atom at and away from resonance.
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    URL: http://dx.doi.org/10.1063/1.526591
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  • 113
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    An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 229-234 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Self-dual Einstein spaces are shown to admit an infinite hierarchy of conservation laws, and this hierarchy is then used to derive a formal version of Penrose's twistor construction. The set of formal holomorphic bundles of fiber dimension 2 over the Riemann sphere P1 is shown to form a formal infinite group which is used to derive nonlinear superposition principles. As an example of our methods a new self-dual Einstein space is obtained as the result of a "collision'' of complex pp-waves "traveling in opposite directions.''
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526652
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  • 114
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    Solution of the Cauchy problem for a generalized sine–Gordon equation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 270-275 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a spectral problem generating a hierarchy of nonlinear evolution equations including the sine-Gordon equation and a physically interesting generalization in the laboratory coordinates. The direct and inverse problems are treated. The time evolution of the spectral data is explicitly given and, therefore, the Cauchy problem for the related equations is solved.
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    URL: http://dx.doi.org/10.1063/1.526656
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  • 115
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    Weakly convergent expansions of a plane wave and their use in Fourier integrals (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 276-291 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Fourier transform of an irreducible spherical tensor is normally computed with the help of the Rayleigh expansion of a plane wave in terms of spherical Bessel functions and spherical harmonics. The angular integrations are then trivial. However, the remaining radial integral containing a spherical Bessel function may be so complicated that the applicability of Fourier transformation is severely restricted. As an alternative, the use of weakly convergent expansions of a plane wave in terms of complete orthonormal sets of functions is suggested. The weakly convergent expansions of a plane wave are constructed in such a way that their application in Fourier integrals leads to expansions of the Fourier or inverse Fourier transform that converge with respect to the norm of either the Hilbert space L2(R3) or the Sobolev space W(1)2(R3). Accordingly, these weakly convergent expansions may be viewed as distributions that are defined on either L2(R3) or W(1)2(R3). The properties of some complete orthonormal sets of functions, in particular their Fourier transforms, are also studied. Shibuya and Wulfman [Proc. R. Soc. London Ser. A 286, 376 (1965)] derived an expansion of a plane wave involving the four-dimensional spherical harmonics. It is shown that this Shibuya–Wulfman expansion is also a distribution which is defined on the Sobolev space W(1)2(R3). Finally, as an application it is shown how weakly convergent expansions can be used profitably for the construction of addition theorems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526970
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  • 116
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    Lie symmetries of some equations of the Fokker–Planck type (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3042-3047 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The structure of the local Lie groups of symmetries of some partial differential equations of the Fokker–Planck type in one space dimension is investigated. A connection between these groups and the group SL2(R) is established in the sense that they are all shown to be locally isomorphic to SL2(R)A, where A is the radical. It is conjectured that the groups of Lie symmetries of all Fokker–Planck equations in one space dimension have this structure. The notion of partial invariance, due to Ovsiannikov, is applied to the equations studied. It appears plausible that the class of partially invariant solutions of these equations is larger than the class of invariant solutions although no explicit demonstration of this claim is available at present.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526681
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  • 117
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    The infinite coupling limit of perturbative expansions from a variational extrapolation method (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3048-3052 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A method for extrapolating perturbative power series to infinity is described. It is a Borel partial resummation stabilized by a variational parameter. Two kinds of series relative to the anharmonic oscillators ||x||k, k〉0, are extrapolated in order to illustrate the effectiveness of the method: the Rayleigh–Schrödinger series, on the one hand, which, after extrapolation, provides the strong coupling expansion of the energy levels, and their lattice expansion, on the other hand, from which is extracted the continuum limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526682
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  • 118
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    Integrable Hamiltonian systems with velocity-dependent potentials (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3070-3079 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The integrability of a two-dimensional Hamiltonian in which the potential depends explicitly on the momenta is investigated. Hamiltonians of this kind are encountered in the description of the motion of a particle in a magnetic field. Two integrable classes of potentials are identified and the second integral of motion is constructed for each of them. The singularity analysis of the equations of motion is also performed, confirming once more the relation between the (weak) Painlevé property and integrability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526685
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  • 119
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    Exact reduced density matrices for a model problem (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3105-3108 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The reduced density matrices of arbitrary order for the boson problem of N particles, each attracted harmonically to a central point and interacting with each other harmonically, are analytically calculated.
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    URL: http://dx.doi.org/10.1063/1.526688
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  • 120
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    Finite-dimensional representations of the Lie superalgebra sl(1,3) in a Gel'fand–Zetlin basis. I. Typical representations (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1640-1660 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In a series of two papers all finite-dimensional irreducible representations of the special linear Lie superalgebra sl(1,3) are constructed. Explicit formulas for the generators in an orthonormal Gel'fand–Zetlin basis of the even subalgebra gl(3) are given. This paper develops a background for constructing the representations. Expressions for the transformation properties of the basis under the action of the generators are written down within all typical sl(1,3) modules.
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    URL: http://dx.doi.org/10.1063/1.526930
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  • 121
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    Transition matrix of point interactions as the scaling limit of integrable potentials on the real line (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1675-1679 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: On the real line, the transition matrix corresponding to the nonrelativistic one-particle Hamilton operator for a finite number of zero-range interaction points is the scaling limit of the transition matrix for corresponding integrable potentials.
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    URL: http://dx.doi.org/10.1063/1.526880
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  • 122
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    Scattering theory for long-range systems at threshold (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1661-1674 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Scattering theory is discussed for long-range systems around threshold, taking into account explicitly the possibility of zero-energy eigenstates of the underlying Schrödinger Hamiltonian. Low-energy expansions are derived for the scattering amplitude in the different cases. The Coulomb-modified scattering length and effective range parameter are defined directly in terms of the scattering amplitude. Explicit formulas for these quantities are provided. No spherical symmetry of the interaction is assumed.
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    URL: http://dx.doi.org/10.1063/1.526963
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  • 123
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    Quantization of systems with many degrees of freedom by the method of collective coordinates: Quantum mechanics around a classical periodic orbit (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1680-1694 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A fairly complete perturbation theoretical solution of the Schrödinger equation around a classical periodic orbit is given as an example demonstrating the quantization of a system with many degrees of freedom by the method of collective coordinates. In particular, explicit expressions are derived for the creation and annihilation operators of quantum fluctuations orthogonal to the classical path, as well as the corresponding eigenfunctions, in both the adiabatic and nonadiabatic domains. It is also shown that corresponding expressions become proportional (and thus can be linked) in domains where they overlap. Finally the splitting of asymptotically degenerate states, and hence the band structure of the resulting spectrum, is calculated.
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    URL: http://dx.doi.org/10.1063/1.526961
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  • 124
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    On the relation between gauge theories, moving frames, fiber bundles, and parastatistics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1695-1700 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We write down standard gauge field theory in a basis-independent manner using the ideas of moving frames (fiber bundles). Then we describe the construction of frames for gauging parafields. To do this (frames) bases for fields are replaced by Clifford matrices. These matrices are in one-to-one correspondence with the number of spinor components. We briefly examine the objects upon which they can act (through matrix multiplication on the left). These objects bear the same relations to spinors that spinors do to vectors. Finally, we show how to construct a set of inner products for the parabases that yield the same action and n-point functions as in the standard field theory.
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    URL: http://dx.doi.org/10.1063/1.526881
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  • 125
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    Solution of the Schrödinger equation for a particle in an equilateral triangle (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2784-2786 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The complete solution for the quantum-mechanical problem of a particle in an equilateral triangle is derived. By use of projection operators, eigenfunctions belonging explicitly to each of the irreducible representations of the symmetry group C3V are constructed. The most natural definition of the quantum numbers p and q includes not only integers but also nonintegers of the class (1)/(3) and (2)/(3) modulo 1. Some relevant features relating to symmetry and degeneracy are also discussed.
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    URL: http://dx.doi.org/10.1063/1.526701
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  • 126
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    Spectral sum rule for time delay in R2 (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2796-2802 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A local spectral sum rule for nonrelativistic scattering in two dimensions is derived for the potential class v∈L4/3 (R2). The sum rule relates the integral over all scattering energies of the trace of the time-delay operator for a finite region Σ⊆R2 to the contributions in Σ of the pure point and singularly continuous spectra.
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    URL: http://dx.doi.org/10.1063/1.526704
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  • 127
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    On the covariance of Dirac's modified canonical commutation relations for fermions interacting with gravity and bosons (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2827-2835 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For fermions in curved space-time, where i(h-dash-bar)ψ° is no longer the canonical conjugate of ψ, canonical quantization according to Dirac requires use of "modified'' graded commutation relations, in which the canonical conjugates to the tetrad field components are no longer commutative with each other or with the fermion field. As shown earlier by the DeWitts, these modified commutation relations may be understood as a canonical quantization of new field variables that can conventionally be interpreted in terms of creation and annihilation operators. Because of the horrible transformation properties of these new variables, covariance of this quantization of fermion fields and of the gravitational field with which the fermions interact is best proved in terms of the old variables. Like canonical quantization, also this modified quantization requires alteration of the theory destroying general invariance of the Lagrangian. As discussed in a preceding paper, covariance of this modified quantization under a group of finite transformations will follow, under the conditions that (1) it can be proved for a generator T1, linear in infinitesimal descriptors of the transformations, that by these modified commutation relations it will generate the substantial variations of the canonical field variables, while (2) the second-order generator T12, constructed from T1 as previously discussed, will be conserved and invariant. It is here proved that these two conditions are satisfied, provided that the transformations leave the Lagrangian function L invariant. This restriction limits the proof of covariance of quantization to affine transformations only. It is discussed why this yet leaves the possibility of general covariance of the "physical part'' of this quantization procedure.
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    Confined gravitational fields produced by anisotropic fluids (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2847-2849 
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    Notes: A family of solutions of the Einstein equations for a spherically symmetric distribution of anisotropic matter is presented, which can be matched with the flat (Minkowskian) space-time on the boundary of the matter, although the energy density and stresses are nonvanishing within the sphere.
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    Collision-free gases in spatially homogeneous space-times (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2869-2880 
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    Notes: The kinematical and dynamical properties of one-component collision-free gases in spatially homogeneous, locally rotationally symmetric (LRS) space-times are analyzed. Following Ray and Zimmerman [Nuovo Cimento B 42, 183 (1977)], it is assumed that the distribution function f of the gas inherits the symmetry of space-time, in order to construct solutions of Liouville's equation. The redundancy of their further assumption that f be based on Killing vector constants of the motion is shown. The Ray and Zimmerman results for Kantowski–Sachs space-time are extended to all spatially homogeneous LRS space-times. It is shown that in all these space-times the kinematic average four-velocity ui can be tilted relative to the homogeneous hypersurfaces. This differs from the perfect fluid case, in which only one space-time admits tilted ui, as shown by King and Ellis [Commun. Math. Phys. 31, 209 (1973)]. As a consequence, it is shown that all space-times admit nonzero acceleration and heat flow, while a subclass admits nonzero vorticity. The stress πij is proportional to the shear σij by virtue of the invariance of the distribution function. The evolution of tilt and the existence of perfect fluid solutions is also discussed.
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    Spacelike conformal Killing vectors and spacelike congruences (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2881-2901 
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    Topics: Mathematics , Physics
    Notes: Necessary and sufficient conditions are derived for space-time to admit a spacelike conformal motion with symmetry vector parallel to a unit spacelike vector field na. These conditions are expressed in terms of the shear and expansion of the spacelike congruence generated by na and in terms of the four-velocity of the observer employed at any given point of the congruence. It is shown that either the expansion or the rotation of this spacelike congruence must vanish if Dna/dp =0, where p denotes arc length measured along the integral curves of na, and also that there exist no proper spacelike homothetic motions with constant expansion. Propagation equations for the projection tensor and the rotation tensor are derived and it is proved that every isometric spacelike congruence is rigid. Fluid space-times are studied in detail. A relation is established between spacelike conformal motions and material curves in the fluid: if a fluid space-time admits a spacelike conformal Killing vector parallel to na and naua =0, where ua is the fluid four-velocity, then the integral curves of na are material curves in an irrotational fluid, while if the fluid vorticity is nonzero, then the integral curves of na are material curves if and only if they are vortex lines. An alternative derivation, based on the theory of spacelike congruences, of some of the results of Collins [J. Math. Phys. 25, 995 (1984)] on conformal Killing vectors parallel to the local vorticity vector in shear-free perfect fluids with zero magnetic Weyl tensor is given. The necessary and sufficient condition for vortex lines to be material lines is derived and the restriction this places on the flow of a thermodynamical perfect fluid is determined. As an application, a pure magnetic field in a rotational fluid is considered and results similar in nature to Ferraro's law of isorotation are obtained. Throughout, corresponding results for a timelike conformal motion and for Newtonian theory are given for comparison.
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    Erratum: New inequalities for the Coulomb T matrix in momentum space [J. Math. Phys. 25, 3033 (1984)] (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3016-3016 
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    Supertwistor realization of SU(2,2/1) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1828-1833 
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    Notes: A space of supertwistors is introduced as a graded vector space by starting with ordinary twistor space multiplied with even Grassmann coefficients and combining it by an othogonal direct sum with a one-dimensional space multiplied with odd Grassmann coefficients. A treatment of the algebraic properties of supertwistor space and of Grassmann-linear transformations on this space lead to a systematic procedure for deriving the structure equations for the graded Lie algebra su (2,2/1).
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    Supertwistor fiber bundles as a formalism for supergravities (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1834-1846 
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    Notes: A gauge theory of supergravity which allows one to obtain first-order Lagrangians that are locally gauge invariant by construction is presented. The formalism makes use of supertwistors as a representation space for the construction of a typical fiber of a vector bundle associated with a principal bundle, where the structural group is the super-Poincaré group. The approach proposed provides a means of resolving one of the central problems of gauge field theories of external symmetry groups, that is the satisfactory treatment of translations.
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    Gauge fixing and Gupta–Bleuler triplets in de Sitter QED (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1847-1854 
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    Topics: Mathematics , Physics
    Notes: Binegar et al. recently developed de Sitter QED within the frame of a particular gauge fixing c= (2)/(3) . Such a choice leads to the simplest possible structure of the Gupta–Bleuler triplets, with the SO(3,2) representations D(3,0) and D(1,1) appearing to describe special gauge solutions. The present work examines the general case c≠ (2)/(3) by considering explicitly the corresponding homogeneous propagators and some fundamental carrier states for the related indecomposable representations of SO(3,2). The latter expressions involve "logarithmic'' gauge states which independently carry extensions of the D(3,0) and D(1,1) Lie algebra representations.
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    On a computation formula for the representation matrices of U(n) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2480-2484 
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    Notes: A d-matrix element of U(n), which is called the semi-highest-weight d-matrix element and plays an essential role for the D-matrix elements, is explicitly determined. By using the result, a formula of computing the D-matrix elements of U(n) is given in terms of lowering operators corresponding to those of Nagel and Moshinsky.
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    Deficiency indices and singular boundary conditions in quantum mechanics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2520-2528 
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    Notes: We consider Schrödinger operators H in L2(Rn), n ∈ N, with countably infinitely many local singularities of the potential which are separated from each other by a positive distance. It is proved that due to locality each singularity yields a separate contribution to the deficiency index of H. In the special case where the singularities are pointlike and the potential exhibits certain symmetries near these points we give an explicit construction of self-adjoint boundary conditions.
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    On the semiclassical description of N-level systems interacting with radiation fields (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2529-2539 
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    Notes: It is shown that the dynamics of an N-level quantum system driven by a classical radiation field can be derived rigorously from an associated fully quantum-mechanical model with the help of an asymptotic limit. By formally expanding the full quantum dynamics around the semiclassical limit, quantum corrections to the semiclassical description are systematically constructed. The observables describing these corrections are shown to exist in any order, and explicit expressions for their time dependence are given.
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    Spectral properties of the Dirac equation with anomalous magnetic moment (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2556-2559 
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    Notes: Though the electron possesses an anomalous magnetic moment, this term has so far been treated by perturbation methods only. Here this rather singular term is treated nonperturbatively. For a general and large class of spherical potentials it is shown that the Hamiltonian is essentially self-adjoint. If the potentials vanish at infinity the essential spectrum is R(backward-slash)(−m,m). These results hold for all, also strong, Coulomb-type potentials. We further establish that the eigenvalues for such Hamiltonians are stable and can be computed by a low-order perturbation theory, if l≥3. The above results can also be extended to multicenter potentials.
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    Is perturbation theory misleading in general relativity? (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2581-2588 
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    Notes: Two senses in which the perturbation equations of general relativity can be misleading are explored. (i) Under certain circumstances there exist solutions of the perturbation equations that appear to be gauge, in that the metric perturbation is the symmetrized derivative of a vector field, but which nonetheless are not true gauge. (ii) Under certain circumstances there exist solutions of the perturbation equations that cannot, even locally, be extended to higher order in perturbation theory. The latter is a local version of the well-known phenomenon of "linearization instability.''
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    Hopf bifurcation in Yang–Mills mechanics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2643-2647 
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    Notes: The periodic non-Abelian space-independent solutions to Yang–Mills SU(2) equations are studied. Hopf bifurcation is shown to appear. New analytic solutions generating a simple Abelian source are found and their stability is discussed. The source can be produced by a fermion field; a self-consistent solution of Yang–Mills–Dirac equations is presented.
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    On extensions of supersymmetry algebras in d=4 and 11 (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2659-2665 
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    Notes: SUSY algebras, in d=4 and 11, are analyzed, extended by the addition of both spinorial and bosonic central charge generators. It is found that only limited extensions are possible, on use of Jacobi identities. Casimirs, irreps, and spin reduction are discussed, and the problems of constructing actions for SUSY and supergravity theories as full superspace actions are considered.
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    A general approach to the systematic derivation of SO(3) shift operator relations. I. Theory (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 128-132 
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    Notes: A new technique is established for the construction of relations between products consisting of two, three, or more SO(3) shift operators, within the framework of the Lie algebras of SO(3) tensor operators constructed out of an underlying single-boson structure.
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    Finite hard rod systems and their thermodynamic limit. III. Collision frequency, no-collision probability, and velocity autocorrelation function (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2617-2626 
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    Topics: Mathematics , Physics
    Notes: We use the methods developed for the one-dimensional hard rod gas in the preceding papers to derive exact expressions for the average number of collisions per unit time, the probability that a tagged particle does not collide with other ones within a given time interval, and the velocity autocorrelation function. It is discussed how these expectation values, obtained for finite systems and three kinds of ensembles (smallest stationary, microcanonical, and canonical), behave as the size of the system increases (thermodynamic limit).
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    A local limit theorem for strongly dependent random variables and its application to a chaotic configuration of atoms (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1165-1172 
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    Notes: We investigate one-dimensional chaotic configurations of atoms, which are generated by the Baker transformation or, equivalently, by the Bernoulli shift. The problem of calculating the distribution of the jth nearest-neighbor distances of these configurations is shown to be equivalent to the task of finding the limit distribution of the sum of the strongly dependent random variables Xl:([0,1),μL)→[0,1), x→(2lx)mod 1 (l∈N0, μL is the Lebesgue measure). We prove the validity of a local limit theorem for this sequence of random variables and conclude, therefore, that the distribution density Gj of the jth nearest-neighbor distances is asymptotically (as j→∞) a Gaussian distribution, the width of which grows as (j)1/2. With the aid of this result, we prove that the pair distribution function G of our configurations, which is the sum of the Gj's, tends to unity in the limit of large distances.
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    Generalization of the diffusion equation by using the maximum entropy principle (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1173-1174 
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    Notes: By using the so-called maximum entropy principle in information theory, one derives a generalization of the Fokker–Planck–Kolmogorov equation which applies when the n first transition moments of the process are proportional to Δt, while the other ones can be neglected.
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    On the wave operator in few-body quantum scattering with Coulomb-like interactions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 139-142 
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    Notes: Functional analytical methods like strong approximation of operator-valued functions and Dunfords' calculus are applied to yield a contour integral representation with a finite contour of wave operators for nonrelativistic potential scattering with Coulomb and short-range interactions, which avoids high singularities of Coulomb-like Green's functions of stationary scattering theory. The Green's function is the unique solution of the resolvent equation, which has an A-proper kernel allowing projector methods for its solution.
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    The short-range expansion for multiple well scattering theory (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 145-151 
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    Notes: We expand the scattering amplitude and the scattering matrix around the zero-range limit, i.e., with point interactions, in the case when the potential has a finite number of wells. The lower-order terms are largely independent of the shape of the potentials.
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    An effective algorithm for obtaining polynomials for dimer statistics. Application of operator technique on the topological index to two- and three-dimensional rectangular and torus lattices (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 157-167 
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    Notes: Recursion formulas on the numbers of ways for placing an arbitrary number of indistinguishable dumbbells on the various rectangular lattice spaces (3×n, 4×n) and torus spaces (2×n, 3×n, 2×2×n) were obtained by the use of the operator technique to the counting polynomial on the topological characteristics (e.g., nonadjacent number, Kekulé number, and topological index). Perfect matching numbers or Kekulé numbers were also obtained for larger lattices such as the 4×n torus and the 2×3×n lattice. By deriving these new results the utility of the proposed method for dimer statistics is demonstrated and some of their mathematical features are discussed.
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    Symmetries of gauge fields (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 192-197 
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    Notes: The concept of homogeneity for a gauge field is introduced as an appropriate geometrical interpretation of the symmetric properties of the gauge field relative to a group of space-time transformations. It is more general than the formulation in terms of an invariant connection, as illustrated by an example on translational symmetries. Sufficient conditions are given for invariance to be equivalent to homogeneity. Both finite and infinitesimal symmetries are treated.
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    Electrodynamics in eight-dimensional space (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 208-210 
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    Notes: Generalized electromagnetic fields and the corresponding generalized electromagnetic field tensor in a real eight-dimensional space-time manifold have been constructed, in terms of which the generalized Maxwell's field equations have been derived. The Lorentz force acting on a charged particle moving in generalized electromagnetic fields has been derived by constructing an eight-velocity vector in this space.
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    Multiplicity-free, unitary and nonunitary irreducible representations of SL(3,R) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 21-28 
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    Notes: Multiplicity-free, irreducible representations of the group ∼(SL(3,R)) are obtained from SU(2) subgroup representations by a constructive method. It is observed that there exist two series of unitary representations with k contents {k0,k0+1,k0+2,...}k0≥3, {k0,k0+2,k0+4,...} k0=0, 1, 1/2 and finite-dimensional representations with k content {k0+1,k0+3,...,k0+2n+1} k0=1, 1/2 {2,4,6,...,2n}, n=1,2,...,k0=0.
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    Vector fields near caustics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1404-1407 
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    Notes: The modified Lagrange manifold technique enables determination of the asymptotic series solution of linear scalar wave equations near caustics of simple geometries. Here the technique is extended to include vector field considerations and more complicated caustic geometries.
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    Erratum: Remarks on canonical transformations in phase-space path integrals [J. Math Phys. 24, 874 (l983)] (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1436-1436 
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    Lie transformation group solutions of the nonlinear one-dimensional Vlasov equation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1428-1435 
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    Notes: The solution of the exact, nonlinear one-dimensional Vlasov equation with a space- and time-dependent electric field is reduced to the solution of a nonlinear, first-order ordinary differential equation with two subsidiary equations. The reduction holds for any electric field nonlinear in the spatial coordinate or for a subclass of electric fields linear in the spatial coordinate and is equivalent to the solution of a generalized Bernstein–Greene–Kruskal (BGK) Vlasov equation with a velocity-dependent Lorentz force. The Lie method for the solution of differential equations invariant under a transformation group has been used to calculate the group generator, the canonical variables, and the generalized BGK Vlasov equation. Analytical forms for the functional dependence of the Vlasov equation one-particle distribution function are given.
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    Dual physical interpretation of the energy tensor: Nonexistence of the Kerr–Newman example (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1021-1023 
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    Notes: Several recent papers have dealt with the possibility of interpreting the Kerr–Newman metric as a viscous fluid as well as its usual interpretation of a rotating, charged black hole. In this paper we show that there is no possible viscous fluid with the Kerr–Newman metric.
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    The relationship between monopole harmonics and spin-weighted spherical harmonics (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1030-1033 
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    Topics: Mathematics , Physics
    Notes: We compare two independent generalizations of the usual spherical harmonics, namely monopole harmonics and spin-weighted spherical harmonics, and make precise the sense in which they can be considered to be the same. By analogy with the spin-gauge language, raising and lowering operators for the monopole index of the monopole harmonics can immediately be written down.
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    Separability of the Dirac equation in a class of perfect fluid space-times with local rotational symmetry (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1034-1039 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: Chandrasekhar's technique for separation of the Dirac equation in the Kerr background is applied to perfect fluid space-times with local rotational symmetry. These space-times fall into three distinct types. It is found that in case (1) the Dirac equation separates if the space-time is at least "locally static'' while in case (3) it separates if the space-time is at least "locally diagonal,'' in contrast to the massless case where Dhurandhar, Vishveshwara, and Cohen showed that the Hertz potential is separable in all cases. In case (2), however, the Dirac equation is separable in all those cases where the Hertz potential for neutrinos is separable.
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    Equilibrium states of inhomogeneous mean-field quantum spin systems with random sites (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1049-1056 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: For inhomogeneous mean-field quantum spin systems with random sites, we prove that the weak*-limit points of the sequence of n-particle Gibbs states, on a suitable C*-algebra, are superpositions of inhomogeneous product states, which are given by solutions of a generalized Curie–Weiss equation. Under certain conditions there is only one weak*-limit point. As applications, the BCS model and a spin system with cosine interaction are studied.
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    Proof of the decoupling theorem of field theory in Minkowski space. II. Theories involving particles with vanishingly small masses (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1065-1069 
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    Topics: Mathematics , Physics
    Notes: The decoupling theorem of quantum field theory is studied in Minkowski space for theories which on experimental grounds may contain particles with vanishingly small masses. Rules are set up to prove the distributional vanishing property of the renormalized amplitudes when any subset of the underlying masses is scaled to infinity, and any subset of the remaining masses is scaled to zero. By careful estimates, the analysis in Minkowski space may be reduced to a similar one in Euclidean space. All subtractions of renormalization are carried out at the origin of momentum space with the degree of divergence of a subtraction coinciding with the dimensionality of the corresponding subdiagram.
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    Conformal symmetry and constants of motion (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1072-1076 
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    Topics: Mathematics , Physics
    Notes: Conformal space-time symmetries of electromagnetic fields and potentials are studied in order to determine whole sets of constants of motion when spin- 1/2 charged particles interact with such external electromagnetic fields. The relativistic and nonrelativistic contexts are discussed through the Hamiltonian formalism. In particular, the interesting example of the magnetic monopole field is recovered and related to the recent works of Jackiw and D'Hoker–Vinet.
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    Lagrangian dynamics on higher-dimensional spaces with applications to Kaluza–Klein theories (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1083-1092 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: We review and apply the method of Lagrangian dynamics to particle motion in higher-dimensional spaces. We discuss in detail the case of a Kaluza–Klein theory with coset spaces as fiber. While the total metric we use in general need not allow for Killing vectors, we require that the restriction to the fiber does. We find that for general Jordan–Thiry scalar fields, the geodesic motion in total space is not describable in terms of particle motion in the base manifold with the usual internal charges. The cases when this is possible are discussed. We also consider the geodesic motion in the Sorkin–Gross–Perry Kaluza–Klein monopoles. We find all the conserved quantities and the equations can be integrated by quadrature.
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    A generalization and refinement of Madivanane's theorem on general involutional transformations (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2087-2091 
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    Notes: A result of Madivanane on "quasianticommuting'' complex square matrices, which are roots of the identity matrix, is generalized to linear operators on infinite-dimensional complex vector spaces. A constant which appears in the result is shown to be nonzero by giving a simple formula for its absolute value. Also, a simple formula for the constant itself is given, which is valid for some cases.
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    Nontrivial zeros of weight 1 3j and 6j coefficients: Relation to Diophantine equations of equal sums of like powers (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2092-2095 
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    Notes: The nontrivial zeros of weight 1 3j and 6j coefficients given previously are shown to be the set of all such zeros. The relation of these zeros to the solutions of well-known Diophantine equations is also discussed.
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    Linearization of nonlinear differential equations by means of Cauchy's integral (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 929-939 
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    Notes: It is suggested to transform a class of nonlinear differential equations with a holomorphic type of nonlinearity into linear integrodifferential equations. The method is presented in detail for first-order ordinary differential equations. The transformed equation is studied and is found to have a unique solution with an analytical representation. In a numerical test calculation rapid convergence of an approximate solution of the linearized equation towards the reference solution is found. The method can be applied to higher-order ordinary and partial differential equations. The transformation can be generalized also to operator-valued differential equations.
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    The Hamiltonian structure of a complex version of the Burgers hierarchy (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 943-945 
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    Topics: Mathematics , Physics
    Notes: In this paper we construct a class of integrable Hamiltonian nonlinear evolution equations generated by a purely differential recursion operator. It turns out that this hierarchy is a complex version of the Burgers hierarchy and can be linearized through a generalization of the Cole–Hopf transformation.
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    Numerical integration in many dimensions. I (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 951-954 
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    Notes: If a d-dimensional integral involves an integrand of the functional form F( f1(x1)+f2(x2)+⋅⋅⋅), then one can introduce an integral transform (Fourier or Laplace or variants on those) which allows all the integrals over the coordinates xi to factor. Thus a d-dimensional integral is reduced to a one-dimensional integral over the transform variable. This is shown to be a very powerful and practical numerical approach to a number of problems of interest. Among the examples studied is the computation of the volume of phase space for an arbitrary collection of relativistic particles. One important aspect of the approach involves numerical integration along various contours in the complex plane.
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    A summation method for the Rayleigh–Schrödinger series for the anharmonic oscillator (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 961-964 
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    Notes: We approximate the energy levels of the anharmonic oscillator with any coupling constant by eigenvalues λj( g,T) of the operator −d2/dx2+x2+gVT(x) with VT(x) =x4 when ||x||≤T and VT(x) =T4 when ||x||〉T. The functions λj( g,T) are holomorphic with respect to g in a neighborhood of the non-negative half-axis. The conformal transformation maps this neighborhood onto the unit circle of the complex plane. It gives the summation method for the Rayleigh–Schrödinger series for every g≥0.
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    Strong approximation of time evolution operators for a finite system of oscillators with nonlinear coupling (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 970-972 
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    Topics: Mathematics , Physics
    Notes: We consider a system in three space dimensions consisting of a finite number of oscillators with a nonlinear interaction. Using projectors on N-particle subspaces of the Fock space, we show that the time evolution operator is strongly approximatable by exponentials of self-adjoint finite-rank operators (finite-dimensional Hermitian matrices), which can easily be calculated in the corresponding eigenrepresentation.
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    Branching index sum rules for simple Lie algebras (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2127-2137 
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    Topics: Mathematics , Physics
    Notes: Let L and L0 be a simple Lie algebra and its sub-Lie algebra, respectively. Then, a given irreducible representation ω of L decomposes into a direct sum of irreducible components of L0, which is called the branching rule. The general Dynkin indices introduced earlier satisfy many sum rules for the branching rule. These are found to be strong enough to uniquely determine the branching rule for many cases we have studied. The sum rules are especially useful for cases of exceptional Lie algebras.
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    Boson realization of sp(4). I. The matrix formulation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2107-2123 
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    Notes: Holstein and Primakoff derived long ago the boson realization of a su(2) Lie algebra for an arbitrary irreducible representation (irrep) of the SU(2) group. The corresponding result for su(1,1)≅sp(2) is also well known. This raises the question of whether it is possible to obtain in an explicit, analytic, and closed form, and for any integer d, the boson realization of a sp(2d) Lie algebra for an arbitrary irrep of the Sp(2d) group, which is a problem of considerable physical interest. The case d=2 already illustrates the problem in its full generality and thus in this paper we concentrate on sp(4). The Dyson realization is well known, and the passage to bosons satisfying the appropriate Hermiticity conditions can be done by a similarity transformation through an operator K. What we want, though, is an explicit boson realization for sp(2d) similar to the one that exists for sp(2). In Sec. VI we show how we can get it for sp(4) if the operator K is known. Unfortunately while the matrix form of K2 can be explicitly derived from definite recursion relations, the same cannot be said of K as it involves, in general, the solution of algebraic equations of high degree. Thus the conclusion, corroborated also by a classical analysis where K does not appear, is that an explicit, analytic, and closed boson realization of sp(4), and thus also of sp(2d), is only possible for particular irreps of the corresponding groups.
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    On the phase retrieval problem in two dimensions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2141-2160 
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    Topics: Mathematics , Physics
    Notes: The paper contains a discussion of the phase retrieval problem in two dimensions and proposes criteria to select those resolutions of the discrete ambiguity of the zero trajectories which are compatible with the analyticity in two variables of the scattered field.
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    Evaluation of the self-energy of a droplet interacting via a Yukawa force (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2138-2140 
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    Notes: The binding energy of a homogeneously charged, classical droplet is considered, whose charge elements interact via a Yukawa force. The six-dimensional self-energy integral is reduced to a three-dimensional integral for axially symmetric, but otherwise arbitrarily shaped, droplets. This integral is brought into a form particularly convenient for numerical calculations. Two integrals involving products of Bessel functions are evaluated, which are either not listed in standard tables of integrals or given in an erroneous form.
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    Some nodal theorems for noncentral forces (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2161-2164 
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    Notes: Two lemmas are proved for local noncentral forces in multidimensional space. First, the lowest partial wave for the ground state is nodeless. Second, the lowest partial wave for the first excited state has at least one node. Ballot–Fabre de la Ripelle perturbation theory is also used to show that higher partial waves for the ground state have nodes near the positions of nodes (if any) in the corresponding element of the matrix element of the noncentral potential.
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    Exact symmetries of unidimensional self-similar flow (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2165-2167 
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    Notes: In addition to the symmetries that are known to apply to arbitrary flow, the self-similar equations may present other symmetries of their own. We present here such a symmetry of the self-similar unidimensional flow of an adiabatic inviscid fluid, with arbitrary polytropic index and arbitrary power-law entropy distribution. The new symmetry can be extended to the non-self-similar case if the flow is assumed isentropic. A connection with the theory of Riemann invariants is also discussed.
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    Generalized Stäckel matrices (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2168-2173 
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    Topics: Mathematics , Physics
    Notes: Stäckel and differential-Stäckel matrices are generalized so that the matrix elements may be functions of the derivatives of the dependent variable as well as the independent variable. The inverses of these matrices are characterized and it is shown that for significant classes of linear and nonlinear partial differential equations, variable separation is accomplished via this generalized Stäckel mechanism.
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    Geometrical interpretation of the solutions of the sine–Gordon equation (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2181-2185 
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    Topics: Mathematics , Physics
    Notes: The sine–Gordon equation is known to possess solutions that correspond to solitons, that is, localized entities that maintain their shape after collisions, and have certain properties characteristic of elementary particles. Although the algebraic structure of these solutions is well known, their geometric interpretation as surfaces of constant negative curvature has not been previously illuminated. We discuss these surfaces herein. Curves drawn on these surfaces along the asymptotic directions at each point simulate solutions of the nonlinear wave equation φxx−φtt=sin φ.
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    Modified equations, rational solutions, and the Painlevé property for the Kadomtsev–Petviashvili and Hirota–Satsuma equations (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2174-2180 
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    Topics: Mathematics , Physics
    Notes: We propose a method for finding the Lax pairs and rational solutions of integrable partial differential equations. That is, when an equation possesses the Painlevé property, a Bäcklund transformation is defined in terms of an expansion about the singular manifold. This Bäcklund transformation obtains (1) a type of modified equation that is formulated in terms of Schwarzian derivatives and (2) a Miura transformation from the modified to the original equation. By linearizing the (Ricati-type) Miura transformation the Lax pair is found. On the other hand, consideration of the (distinct) Bäcklund transformations of the modified equations provides a method for the iterative construction of rational solutions. This also obtains the Lax pairs for the modified equations. In this paper we apply this method to the Kadomtsev–Petviashvili equation and the Hirota–Satsuma equations.
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    Harmonic analysis of the Euclidean group in three-space. II (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2186-2188 
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    Notes: We develop the harmonic analysis for spinor functions which are defined by the matrix elements of the unitary irreducible representations of E(3) with the representation space on the translation subgroup.
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    Dynamic systems driven by Markov processes (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2189-2191 
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    Notes: Consider a differential equation Y(overdot)=V(X(t))Y(t), where X(t) is a random function. Sufficient conditions for asymptotic stability of the solution in terms of a generator of the stochastic process X(t) are given. The results are illustrated by several examples.
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    Noncoordinated basis and Schild's solution (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2192-2195 
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    Notes: In this paper we show the paradoxical consequences which appear in Schild's solution, as seen from a noninertial frame (NIF). We propose a treatment for the noninertial frame which resolves the ambiguities.
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    Singularities of the continuation of fields and validity of Rayleigh's hypothesis (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2201-2204 
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    Notes: To formulate general results concerning the validity of the Rayleigh hypothesis, we first introduce a definition of the foci and antifoci of an analytic curve. Then, we state two lemmas on the properties of an analytic or harmonic function satisfying given conditions on an analytic curve. This allows us to predict the behavior of the analytic continuation of the field in electrostatics. The use of a conformal mapping permits the generalization of this method in electromagnetics and acoustics. As a consequence, we are able to predict the limit of validity of the Rayleigh hypothesis.
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    Splitting methods for time-independent wave propagation in random media (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2196-2200 
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    Topics: Mathematics , Physics
    Notes: Time-independent wave propagation is treated in media where the index of refraction contains a random component, but its mean is invariant with respect to translation in some direction distinguishing the wave propagation. Abstract splitting operators are used to decompose the wave field into forward and backward traveling components satisfying a coupled pair of equations. Mode-coupled equations follow directly from these after implementing a specific representation for the abstract splitting operators. Here we indicate a formal solution to these equations, concentrating on the diffusion regime, where we estimate the forward- and backscattering contributions to the mode specific diffusion coefficients. We consider, in detail, random media with uniform (random atmosphere) and square law (stochastic lense) mean refractive indices.
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    Usual and unusual summation rules over j angular momentum (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 728-731 
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    Notes: After recalling the usual j-summation rule over an angular momentum we describe two unusual summation rules. The first one concerns sum of products of "3nj'' and "3j0'' coefficients. The second involves sum of products of "3jm'' coefficients but with the (2j+1) weighting factor missing.
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    Wavelength-dependent electromagnetic parameters for coherent propagation in correlated distributions of small-spaced scatterers (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2208-2217 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Earlier results for coherent propagation of electromagnetic waves in pair-correlated random distributions of scatterers (of radius a and physical parameters ε',μ') with minimum separation of centers b≥2a small compared to wavelength (2π/k) are generalized to obtain polarization, refraction, and absorption terms to order k2. The development includes multiple scattering and multipole coupling by electric and magnetic dipoles, as well as quadrupoles to appropriate order. The correlation aspects are determined by simple integrals of the statistical mechanics radial distribution function f for impenetrable particles (spheres, cylinders, and slabs) of diameter b. For slab scatterers, in terms of the exact Zernike–Prins f, the correlation integrals are expressed as algebraic functions of the volume fraction w; the resultant bulk values reduce to those of one particle at full packing, w=1. Similar results are obtained for spheres in terms of the Wertheim–Thiel solution of the Percus–Yevick approximation of f at the unrealizable bound w=1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526849
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    Path integral quantization of the dyonium (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2231-2233 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The dyonium is solved exactly by path integration. The Green's function for the dyonium is separated into the monopole harmonics and the radial path integral, and the radial Green's function is found in closed form. The exact energy spectrum is also obtained. Dirac's charge quantization condition is seen to be essential for performing path integration.
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    URL: http://dx.doi.org/10.1063/1.526852
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    Core size effects, bound states, and scattering states of the Aharonov–Bohm problem (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2218-2221 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The mathematical solutions of Schrödinger's equation for an electron which is moving outside a hard cylindrical core which contains a hidden flux is studied and it is shown that there are two possible types of eigenstates or scattering states. The first type of state is cyclic about the hidden flux. Such states give rise to field-induced energy shifts, to probability density shifts, and to a divergent scattering cross section. The second type of state is noncyclic about the above axis but all the physical observables are independent of the hidden magnetic flux. The relationship to gauge invariance is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526850
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  • 187
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    Space-times with intrinsic symmetries on the three-spaces t=constant (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 785-791 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider metrics which possess a priori certain "intrinsic symmetries'' on the three-spaces t=const. In the vacuum case, we obtain a generalization of Birkhoff's theorem and a set of solutions with a translational isometry operating on the whole space-time. In the nonvacuum case, we assume a perfect fluid matter content and a fluid flow orthogonal to the three-spaces t=const, and obtain several exact analytical solutions, some of them satisfying the standard energy conditions. In particular, a stiff equation of state is obtained in some cases, and we also have found particular solutions where a plane, spherical, or hyperbolic intrinsic symmetry is manifest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526568
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    Simplicial minisuperspace I. General discussion (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 804-814 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The use of the simplicial methods of the Regge calculus to construct a minisuperspace for quantum gravity and approximately evaluate the wave function of the state of minimum excitation is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526571
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  • 189
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    The statistics of interacting dumbbells on a 2×N lattice space (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 815-821 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A set theoretic argument is utilizied to determine a 31-term recursion that describes exactly the composite nearest-neighbor degeneracy for indistinguishable dumbbell particles distributed on a rectangular 2×N lattice space. The associated generating functions, the expectation of the lattice coverage, and the density of occupied nearest-neighbor pairs are also determined.
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    URL: http://dx.doi.org/10.1063/1.526572
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    Generalization of Weyl's gauge group (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 831-835 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Weyl's gauge transformations in a general n-dimensional Riemannian manifold are extended from the conformal group to GLn(R). The gauge-covariant field generalizing that of the Maxwell tensor is determined. The relationship between Weyl gauging and Yang–Mills gauging is developed. It is shown that the two processes are not equivalent, but can be made compatible.
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    URL: http://dx.doi.org/10.1063/1.526574
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  • 191
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    Gauge fields in algebraically special space-times (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 836-840 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that in an algebraically special space-time which admits a congruence of null strings, a source-free gauge field aligned with the congruence is determined by a matrix potential which has to satisfy a second-order differential equation with quadratic nonlinearities. The Einstein–Yang–Mills equations are then reduced to a scalar and two matrix equations. In the case of self-dual gauge fields in a self-dual space-time, the existence of an infinite set of conservation laws, of an associated linear system, and of infinitesimal Bäcklund transformations is demonstrated. All the results apply for an arbitrary gauge group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526575
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    Scattering by a parabolic cylinder—A uniform asymptotic expansion (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 854-860 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A uniform asymptotic expansion in the variable, determining the location of the observer for the fields scattered by a perfectly conducting parabolic cylinder, is derived. This expansion can be applied to scattering by arbitrary smooth convex surfaces of variable curvature. The accuracy of numerical results is examined.
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    URL: http://dx.doi.org/10.1063/1.526578
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    Torsion of certain beams (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 864-869 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Complex variable methods are introduced to derive exact and closed expressions for the stress functions, torsional rigidities, and peripheral shearing stresses of certain isotropic cylinders under torsion. Numerical results in some special cases are presented in tabular and graphic form. The equations for the boundaries of the cross sections for these cylinders have the polar forms r2=a2(2 cos 2θ−1), a〉0 (||θ||≤π/6), r4=2na4/(n−1+cos 4θ)(n+1+cos 4θ), a〉0 (||θ||≤π, 2〈n〈∞), and rm−2=am−2 (cos2 θ−cos2δ) /sin2 δ cos mθ, a〉0 (m〉2, 0〈δ〈π/2m, ||θ||≤δ).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526580
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    Isotropic homogeneous universe with viscous fluid (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 878-881 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Exact solutions are obtained for the isotropic homogeneous cosmological model with viscous fluid. The fluid has only bulk viscosity and the viscosity coefficient is taken to be a power function of the mass density. The equation of state assumed obeys a linear relation between mass density and pressure. The models satisfying Hawking's energy conditions are discussed. Murphy's model is only a special case of this general set of solutions and it is shown that Murphy's conclusion that the introduciton of bulk viscosity can avoid the occurrence of space-time singularity at finite past is not, in general, valid.
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    URL: http://dx.doi.org/10.1063/1.526582
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    Erratum: On some general properties of the point spectrum of three particles moving in one dimension [J. Math. Phys. 25, 2589(1984)] (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 882-882 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: NONE
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    URL: http://dx.doi.org/10.1063/1.526583
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    Differential characters: The Dirac monopole as an example (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3176-3179 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Choosing the Dirac monopole as an example, the theory of differential characters is sketched and the quantization condition is recovered in a new way without considering singularities and without using a global formulation of gauge fields (i.e., without using fiber bundle techniques).
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    URL: http://dx.doi.org/10.1063/1.526645
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    Simple calculation of Löwdin's alpha function. II. Easier procedure for evaluating bK k(L M||l ), and vanishing of hn,2n−i(L M||l ) for special values of i and n (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 3193-3199 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper subsequent to the one [J. Math. Phys. 25, 1133 (1984)] (referred to as Part I) presents the following new results: It is found out that for M=L and L−1 the coefficients bK k(L M||l) in Löwdin's α-function have properties other than manifested in Part I. The expression for bK k(L M||l) is shown to be equivalent to the one into which Sharma's expression, obtained in a different manner from that in Part I, is simplified by Rashid. The use of Rashid's expression leads to the recurrence formula for bK k(L M||l) with respect to M only. This formula and the expression for the bK k(L M||l) with M=L provide an easier procedure for successively evaluating bK k(L M||l) than in Part I. Furthermore, it is proved that the coefficients hn,2n−i(L M||l) in the asymptotic form of the α-function vanish for i〈l+M and for n〈l.
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    URL: http://dx.doi.org/10.1063/1.526648
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    An inverse problem in crystallography (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2717-2720 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Coordinate-independent formulations are derived for the conditions satisfied by the elastic modulus tensor of materials with trigonal, hexagonal, and cubic symmetry. Analogous results for two-dimensional modulus tensors are also derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526741
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  • 199
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    Classical SU(2) Yang–Mills–Higgs system: Time-dependent solutions by similarity method (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2746-2748 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A similarity analysis of the Wu–Yang–'t Hooft–Julia–Zee-ansatz-reduced system of nonlinear differential equations of classical SU(2) Yang–Mills–Higgs theory is presented. This yields the similarity group G of the equations. Considering G and one of its subgroups denoted G1, some previously known time-dependent solutions in the Prasad–Sommerfield limit are generated. Two new time-dependent solutions are also reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526745
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    On the existence of global integral forms on supermanifolds (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2749-2753 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the Berezin approach to integration on supermanifolds can be applied to cases where the supermanifold is a twisted extension of a real manifold. This is done by showing that supermanifolds admit a subatlas of coordinate charts with transition functions of a quite restricted kind.
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    URL: http://dx.doi.org/10.1063/1.526746
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