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  • Articles  (17,277)
  • 2010-2014
  • 1990-1994  (17,277)
  • 1985-1989
  • 1950-1954
  • 1990  (17,277)
  • Mathematics  (14,249)
  • Technology  (2,046)
  • History  (1,416)
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  • 2010-2014
  • 1990-1994  (17,277)
  • 1985-1989
  • 1950-1954
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  • 1
    Electronic Resource
    Electronic Resource
    High symmetry solutions of the anti-self-dual Yang–Mills equations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2253-2257 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Beginning with the anti-self-dual Yang–Mills (ASDYM) equations for an arbitrary Lie algebra on Minkowski space, this paper specializes to the case in which the vector potentials are independent of all the space-time coordinates, i.e., are space-time constants. The resulting equations are three algebraic equations on the algebra. These equations are then simplified by using a null basis. Two of the equations can be immediately solved while the third remains, in general, quite difficult to deal with. Two general cases are considered: finite-dimensional Lie groups and the infinite-dimensional diffeomorphism groups on finite-dimensional manifolds. In a few of the special cases, e.g., SL(2,C) and the Virasoro algebra, the solutions can easily be found. The study of the the diffeomorphism groups leads unexpectedly to the Monge–Ampère equation. In particular, the four-dimensional volume preserving diffeomorphism group is identical with the vacuum anti-self-dual Einstein equations. In conclusion, the question of the associated Lax pair equations and its relation to the Riemann–Hilbert splitting problem on S2 is examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528633
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  • 2
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    Character formulas for irreducible modules of the Lie superalgebras sl(m/n) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2278-2304 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Kac distinguished between typical and atypical finite-dimensional irreducible representations of the Lie superalgebras sl(m/n) and provided an explicit character formula appropriate to all the typical representations. Here, the range of validity of some character formulas for atypical representations that have been proposed are discussed. Several of them are of the Kac–Weyl type, but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl(3/4). Having ruled out, therefore, all such formulas, a completely new extension of the Kac–Weyl character formula is proposed. The validity of this formula in the case of all covariant tensor irreducible representations is proved, and some evidence in support of the conjecture that it covers all irreducible representations of sl(m/n) is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528637
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  • 3
    Electronic Resource
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    Classical scattering of a charged particle on an extended magnetic monopole (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2305-2313 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The classical equations of motion for a charged particle scattering on an extended magnetic monopole are found in a model that includes the possibility of charge exchange between the particle and the pole. The special case of a spherical shell of monopole density is examined in detail. Deviations from point monopole scattering are analyzed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528638
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  • 4
    Electronic Resource
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    Local supersymmetry in nonrelativistic systems (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2271-2277 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Classical and quantum nonrelativistic interacting systems invariant under local supersymmetry are constructed by the method of taking square roots of the bosonic constraints that generate timelike reparametrization, leaving the action unchanged. In particular, the square root of the Schrödinger constraint is shown to be the nonrelativistic limit of the Dirac constraint. Contact is made with standard models of supersymmetric quantum mechanics through the reformulation of locally invariant systems in terms of their true degrees of freedom. Contrary to the field theory case, it is shown that locally invariant systems are completely equivalent to corresponding globally invariant systems, where the latter are the Heisenberg picture description of the former with respect to some fermionic time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528636
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  • 5
    Electronic Resource
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    Squeezing of free Bose fields (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2327-2333 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The relevant structure of a Bose Fock space using the notion of free commutative algebra with unit element and with a scalar product is incorporated. The squeezed states are then the exponentials of quadratic forms and can be written in the normal form of a general squeeze group. The connection of this group to polarization of the initial Hilbert space is established and its infinitesimal generator is computed. In this way, a common denominator for a series of papers is provided in the topic of light squeezing and last but not least a mathematical formalism is provided that may prove convenient in the general treatment of quantum optics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528640
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  • 6
    Electronic Resource
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    Scattering for step-periodic potentials in one dimension (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2181-2191 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quantum scattering is developed for impurities in potentials that tend to a periodic function in one direction and a constant in the other. Two new technical results are obtained for Hill's equation. Analytic, asymptotic, and spectral properties are established for solutions of the Schrödinger equation for step-periodic potentials, with and without impurity. The properties have all been used in Marchenko–Newton inverse scattering. Results apply feasibly to electron, photon, and phonon propagation in layered media.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528622
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  • 7
    Electronic Resource
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    Higher-dimensional Vaidya metric with an electromagnetic field (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2208-2210 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An exterior solution is obtained for a charged radiating sphere in higher dimensions. The solution reduces to an earlier one obtained by Krori and Barua [J. Phys. A 7, 2125 (1974)] when the space-time dimension is four, and to one obtained by Iyer and Vishveshwara [J. Phys. 32, 749 (1989)] when the electromagnetic field is switched off.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528626
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  • 8
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    Embedding of a Demianski cavity with small rotation parameter in a perturbation of a Friedmann universe with cosmological constant (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2204-2207 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The problem of embedding a Demianski cavity with small rotation parameter in an appropriate rotational perturbation of a pressureless Friedmann universe with a Λ term is considered. The relation between the coordinate change introduced by Schücking [Z. Phys. 137, 595 (1954)] for this kind of problems and that used for the simple model of Oppenheimer and Snyder [Phys. Rev. 56, 455 (1939)] for gravitational collapse is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528625
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  • 9
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    Symmetries of space-time and geodesic symmetries (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2211-2216 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown how to construct symmetries of the geodesic equation starting from space-time symmetries. The constants of motion associated with space-time symmetries are recovered and a few new ones are found using non-Noetherian conservation theorems. Explicit examples are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528627
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  • 10
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    Particle symmetry and antisymmetry in approximately relativistic Lagrangians (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1929-1938 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For a single-time approximation of the type discussed by Woodcock and Havas [Phys. Rev. D 6, 3422 (1972)] applied to particle-asymmetric Poincaré-invariant variational principles (VPs) of the Fokker type, a method is presented for expressing approximately relativistic Lagrangians (ARLs) to any order in c−1 in a form such that coefficients of functions of the instantaneous three-separation rij are either particle symmetric or antisymmetric. These functions of rij are determined solely by the corresponding particle symmetric or antisymmetric parts of the exactly relativistic kernel of the VP describing two-body interactions of N classical point particles. While the exact kernel involving the particles' four-separations and four-velocities is particle asymmetric, the built-in static Newtonian limit is particle symmetric. Using this method to reformulate previously published ARLs to order c−3 makes it obvious that a sufficient condition for acceleration-free ARLs to order c−3 is that the kernel of the exact non-time-reversal-invariant interaction be particle symmetric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528692
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  • 11
    Electronic Resource
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    Nth (even)-order minimum uncertainty products (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1947-1950 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper considers the problem of finding the quantum states that minimize the products of the (even) Nth-order fluctuation of two canonically conjugate operators. The problem is first attacked in an abstract form and an equation derived for the desired states. A consideration of the N=2 case then leads to a connection with the new concept of "squeezed states'' of the electromagnetic field, and the usual exact solution involving the coherent state. The concept of "higher-order squeezing'' is touched on to motivate the further discussion. The cases N=4, 6, and 8 are then taken up, and approximate solutions to them found via a new numerical technique. During these calculations, it is noted that only the first few terms in the expansion in number states figure in the solution; this observation is then exploited to find an approximate closed solution to the problem valid for all N.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528642
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  • 12
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    The generalized continued fractions and potentials of the Lennard-Jones type (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1955-1961 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For a broad class of the strongly singular potentials V(r), which are defined as superpositions of separate power-law components, the general solution of the corresponding Schrödinger differential equation is constructed as an analog of Mathieu functions. The analogy is supported by the use of the (generalized) continued fractions. The questions of convergence are analyzed in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528644
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  • 13
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    Algebraic calculation of the Green's function for the Hartmann potential (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1951-1954 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using the so(2,1) Lie algebra and the Baker–Campbell–Hausdorff formulas, the Green's function for the Hartmann potential is constructed and its bound state energy spectrum is found. Also, this Green's function is constructed in a coherent state basis and the equivalence of the two descriptions is shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528643
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  • 14
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    On redshift and parallaxes in general relativistic kinematical world models (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1962-1971 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A Lorentzian space-time (M,g), along with an observer field (=timelike vector field) V, are considered. Several theorems are presented that are concerned with the redshift and parallaxes in such a model. Here the term "parallaxes'' stands for the relative motion of two observers at the celestial sphere of a third observer. As an important mathematical tool, the index form along a lightlike geodesic is used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528645
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  • 15
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    Internal and external metrics for a perfect fluid cylinder in general relativity (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1972-1973 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A solution to Einstein's equations describing a perfect fluid cylinder of finite radius is presented. The proper density μ and pressure p of the fluid are physically well behaved in the radial coordinate range 0≤r≤r1. On the axis (r=0) the solution is regular and μ and p are finite and positive. As r increases μ and p decrease steadily through positive values, p vanishing at r=r1. The ratio p/μ (〈1) is also monotonically decreasing, as is also the velocity of sound a (〈1) in the fluid. The equation of state is p= (3)/(7) μ−Nμ3/10, where N is a positive constant. The matching metric for the vacuum exterior to the cylinder is given, so that the space-time is complete and nonsingular.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529021
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  • 16
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    A spherical collapse solution with neutrino outflow (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1974-1977 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A three-parameter family of solutions of Einstein's field equations is given that represents a collapsing perfect fluid with outgoing neutrino flux. Solutions with "naked'' singularities are exhibited. They can be forbidden by requiring pressure less than or equal to the density as a condition of cosmic censorship.
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    URL: http://dx.doi.org/10.1063/1.528646
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  • 17
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    Numerical procedures for sample structures on stochastic differential equations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1978-1990 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Procedures are discussed for the numerical construction of sample processes on stochastic differential equations. Structures of a relevant class of Gaussian white-noise functionals are analyzed to some closed forms, and new numerical algorithms for single noise problems are presented up to the accuracy of O(h3), or within errors of O(h7/2), in the sense of the mean-square norm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528647
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  • 18
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    Bispinor geometry for even-dimensional space-time (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1991-1997 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The geometric properties of Dirac spinor fields defined over even-dimensional space-time are explored with the aim of formulating the associated nonlinear sigma models. A spinor field Ψ may be uniquely reconstructed from the real bispinor densities ρi=Ψ¯ΓiΨ, apart from an overall phase, so that the ρi constitute an alternate representation of the physical information contained in Ψ. For space-time of dimension N=2n, the corresponding Dirac spinor has D=2n complex components, and the bispinor densities satisfy a system of (D−1)2 homogeneous quadratic algebraic equations. The basis elements of the Clifford algebra {Γi} span a D2=2N -dimensional space whose Cartan metric is flat pseudo-Riemannian; the bispinor densities reside in the (2D−1)-dimensional curved subspace induced as an embedding by the algebraic constraints. The explicit geometric structure of the bispinor spaces are examined and found to be generalizations of Robertson–Walker space. In particular, the line element may be written as dS2=D dσ 2+σ 2 dΩ2, where σ=Ψ¯Ψ is the scalar density and dΩ is the line element for the homogeneous space: SU(D/2,D/2)/S(U(1)⊗U(D/2−1,D/2)).
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    URL: http://dx.doi.org/10.1063/1.528648
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  • 19
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    Extension of two-body Dirac equations to general covariant interactions through a hyperbolic transformation (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1998-2014 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In previous work, Dirac's constraint mechanics and supersymmetry were used to construct two-body Dirac equations for particles interacting through world scalar and vector potentials. The resulting compatible 16-component wave equations, S1ψ=γ51(γ1⋅(p1−A˜1) +m1+S˜1)ψ=0, S2ψ=γ52(γ2⋅(p2−A˜2) +m2+S˜2)ψ=0, yield Schrödinger-like equations in the center-of-momentum system with simpler structure than that possessed by the Bethe–Salpeter equation or any of its standard three-dimensional truncations. For strong interactions, these equations have yielded a relativistic quark model for meson spectroscopy, while for electromagnetic interactions they have yielded a family of exact singlet positronium solutions. This paper uncovers a hyperbolic interaction structure in these equations. This structure is used to generalize these equations to include pseudoscalar, pseudovector, and tensor interactions.
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    URL: http://dx.doi.org/10.1063/1.528649
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  • 20
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    A new scheme for enumerating connected diagrams on the lattice (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2015-2024 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this article, a scheme based on recursive generation of connected diagrams is proposed for enumerating the connected diagrams in various expansions for lattice field theories. This scheme is rigorous and general, and can be applied to the analytical methods in various lattice field theories. Some notions and results of the modern graph theory in mathematics are used. As examples, the diagram theoretic factors that occur in the average link energy of the lattice chiral field model and in the external source parameter of the pure lattice gauge field model are calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528650
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  • 21
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    On a Lie algebra of vector fields on a complex torus (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2033-2034 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper discusses a modification of the Krichever–Novikov Lie algebra of vector fields on the torus in which the two specified points where singularities can occur are points of order 1 and 2 rather than points of infinite order.
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    URL: http://dx.doi.org/10.1063/1.528652
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  • 22
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    U(2) extension of modified Bessel function with two indices (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2025-2032 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new set of functions that are given by the coefficients of the character expansion of the single-link action in the U(2) lattice gauge theory is studied. The set relies on the introduction of the character of the mixed term of the normal and adjoint U(2) variables. From the Schwinger–Dyson variational method the recursion relations among the functions are derived. From the relations the asymptotic behaviors of the function at the inverse coupling →0 and ∞ are derived. Through the combination of the recursion relations and the differentiation the linear differential equation of the fourth order is derived. The properties of the solution are discussed.
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    URL: http://dx.doi.org/10.1063/1.528651
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  • 23
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    Superconformal algebra of meromorphic vector fields with multipoles on a super Riemann sphere (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2040-2041 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The superconformal algebras of meromorphic vector fields with multipoles and the relevant Abelian differential of the third kind on a super Riemann sphere were constructed. The algebra includes two Ramond sectors as subalgebras.
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    URL: http://dx.doi.org/10.1063/1.528654
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  • 24
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    A class of integral transforms associated with the Majorana representation of SL(2,C) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2035-2039 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the boson operators for the Majorana representation of SL(2,C) realized as hyperdifferential operators in the Bargmann Hilbert space of analytic functions yield, on exponentiation, a parametrized continuum of integral transforms. Each value of the group parameters yields an integral transform pair. The formula for the inversion of the transform is obtained simply by replacing the group element by its inverse.
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    URL: http://dx.doi.org/10.1063/1.528653
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  • 25
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    Relativistic relaxation models for a simple gas (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2042-2046 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general relativistic time-relaxation model is introduced and compared with the relativistic Boltzmann equation. It is proved that the model has the same features (formal properties of linear operator, positive transport coefficients, etc.) of the Boltzmann equation. It is also shown that the phase speed of infinitesimal disturbances, propagating in a gas described by our model, is less than the speed of light.
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    URL: http://dx.doi.org/10.1063/1.528655
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  • 26
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    Effective conductivity and average polarizability of random polycrystals (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2047-2056 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A third-order expansion for the effective thermal conductivity tensor @sK* of anisotropic polycrystalline cell materials is derived. The coefficients of the expansion are given in terms of the average polarizability tensor, a nondimensional quantity determined from the grain shape and crystallographic orientation distributions independent of other details of the microgeometry such as two (or more) particle correlation functions. Explicit numerical results for a wide variety of microgeometries made of ellipsoidal cells are obtained. This calculation uses a new method that exploits the symmetry properties of the effective conductivity tensor of a cell material as a function of the single-crystal conductivities.
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    URL: http://dx.doi.org/10.1063/1.528656
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  • 27
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    Multivariable biorthogonal continuous–discrete Wilson and Racah polynomials (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1559-1575 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented. These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables. The latter are referred to as the multivariable biorthogonal Racah polynomials. Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials.
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    URL: http://dx.doi.org/10.1063/1.528697
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  • 28
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    The unitary irreducible representations of SU(2,1) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1576-1586 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper analyzes the irreducible unitary representations of SU(2,1) in a basis labeled as ||p, q; jmy〉, where p,q correspond to quantum numbers associated with the quadratic and cubic Casimir operators, j,m label states of the SU(2) subgroup, and y labels the quantum number with respect to the U(1) subgroup. All the irreducible representations are found and the allowed range of these quantum numbers for each representation are given. The results are expressed in the form of diagrams that show the allowed values in a (j,y) plot for fixed values of p,q. A (p,q) plot is also provided that indicates the allowed values of these quantum numbers.
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    Symplectic orbits in quantum state space (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1587-1588 
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    Notes: All symplectic orbits of the action of an arbitrary compact connected Lie group on the space of density operators are found. It is shown that there is only one orbit that is Kähler (orbit of coherent states).
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    Relationship between SN and U(n) isoscalar factors and higher-order U(n) invariants (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1589-1599 
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    Notes: General relationships expressing U(n) and SN coupling and transformation isoscalar factors in terms of U(n) Racah and 9λ coefficients are derived. The absolute values of U(n) Racah coefficients involving at most k-column irreducible representations are shown to be identical with SU(k) Racah coefficients. In particular, an explicit relationship is established between the U(n) and SU(2) approaches to the many-electron correlation problem.
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    Remarks on tensor operators (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1605-1609 
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    Notes: The notion of an algebra of tensor operators for a simple Lie algebra is discussed. A model for the finite-dimensional irreducible representations of sl(4) is constructed. Explicit Wigner operators acting on the model are defined. Striking commutation properties for these operators are conjectured that resolve a sequence of nontrivial multiplicity problems.
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    On some Racah coefficients of U(n) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1600-1604 
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    Topics: Mathematics , Physics
    Notes: Some U(n) Racah coefficients appearing in various applications of vector coherent state and K-matrix theories are calculated: For such a purpose, use is made of their definition in terms of U(n):U(n−1) reduced Wigner coefficients and U(n−1) Racah coefficients. By starting from known U(2) Racah coefficients, the recursion relations obtained are solved by induction over n.
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    Moment invariants for the Vlasov equation (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1610-1615 
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    Notes: Moment invariants [functions of the moments of a Vlasov distribution that are invariant under Sp(6)] are classified using Young diagrams. The connection between the moment invariants and the Poincaré invariants is established. An application using the moment invariants as phase space coordinates is considered for a matching section in a particle-beam accelerator, and a Lie–Poisson numerical integration algorithm for the moment dynamics is proposed.
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    Nonlinear evolution equations related to the first-order system: φx =λJφ+Pφ (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1616-1620 
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    Notes: Let Ut =F(U,∂U/∂x,..., ∂rU/∂xr,t) or Uxt =F(U,∂U/∂x,...,∂rU/∂xr,t) be the nonlinear evolution equations that are the compatibility conditions between φx =λJφ+Pφ and φt =Aφ for P=U(x,t) or P=Ux(x,t), respectively. In this paper, it is proved that if A(Z0,...,Zr−1,t,λ) is a continuous function such that (∂A/∂Zk) (Z0,...,Zr−1,t,λ) k=0,1,..., exists (Zk=∂kU/∂xk), then for P=U(x,t), A is a polynomial in λ of degree r and for the case P=Ux, A=A−1/λ+A0+⋅⋅⋅+Ar−1λr−1. The case where P=Zm, m≥2 is also analyzed.
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    Relations between hyperspherical harmonic transformations and generalized Talmi–Moshinsky transformations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1621-1626 
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    Topics: Mathematics , Physics
    Notes: The correlations between the hyperspherical harmonic transformations and the generalized Talmi–Moshinsky transformations are studied for the three-body and four-body systems. An optical approach for solving few-body problems through diagonalizing the Hamiltonian of a system in an optimal subset of the basis functions of harmonic oscillators in hyperspherical coordinates is proposed. The evaluations of the interaction matrix elements are achieved with the aid of the transformation properties of hyperspherical harmonics.
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    Exponentially evolving densities (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1632-1634 
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    Notes: The notion of a conserved density is generalized to those densities whose integrals evolve exponentially. In the formal differential algebra used to find them, only a slight modification of the conserved density case is needed. Various examples for quasilinear evolution equations are given and an application to finding higher-order conserved densities by taking the Poisson bracket of exponentially evolving densities is indicated.
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    Lie group symmetries and invariants of the Hénon–Heiles equations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1627-1631 
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    Notes: Lie group symmetries and invariants of the generalized Hénon–Heiles equations are found. The coupled second-order equations are invariant under translations in time, in general, and the stretching group (dilation) if the linear terms in the "force'' are absent. The equivalent set of four coupled first-order equations is found to be invariant under a one-parameter group for three cases and the group generators are given. Three different approaches are reported: the "classical method'' for determining Lie group symmetries, a modified method for finding Lie group symmetries with vector fields and the direct method for calculating the invariants. For the Hénon–Heiles equations the direct method is the most efficient.
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    Equivariant harmonic maps into homogeneous spaces (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1635-1642 
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    Notes: This paper is about harmonic maps from closed Riemann surfaces into homogeneous spaces such as flag manifolds and loop groups. It contains the construction of a family of new examples of harmonic maps from T2=S1×S1 into F(n) or Ω(U(n)) that are not holomorphic with respect to any almost complex structure on F(n) or Ω(U(n)), where F(n) is the quotient of U(n) by any maximal torus and Ω(u(n)) consists of f: S1→U(n) smooth such that f(1)=I.
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    Parabose algebras and subgraph polynomials (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1652-1656 
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    Notes: A graph theoretical method is proposed for the calculation of inner products in the Fock spaces of parabose algebras. For this purpose, a new class of polynomials associated with finite graphs is introduced. The obtained results can be generalized to the parafermi case.
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    Hannay's angles outside the adiabatic range: Coupled linear oscillators near resonance (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1657-1660 
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    Notes: The simple harmonic 2-degree of freedom (dof) oscillator with the potential V= (1)/(2) [(1+r sin εt)q21+(1−r sin εt) q22+2r cos εtq1q2] is considered. It is shown that a coupling parameter k∼r/ε determines the behavior of the system after a loop 0≤t≤2π/ε in parameter space. Somewhat unexpected mode conversion and phase corrections occur. An optical model is outlined.
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    Geometry of linear pairs for self-dual gauge fields (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1643-1651 
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    Notes: A linear pair for self-dual gauge fields is constructed for the metric ds2=gzz¯dzdz¯+gyy¯dyd¯. It is shown that for consistency gzz¯ and gyy¯, apart from a possible overall conformal factor, are given in terms of two Liouville fields of equal and opposite curvatures. The null surface corresponding to the pair and the homogeneous solutions, playing a fundamental role, are constructed explicitly. The five-dimensional space of y,y¯,z,z¯ and the spectral parameter λ is studied. The proper transformation of λ corresponding to holomorphic ones of y and z is found. Known monopole, instanton, and (quasi)periodic solutions are all shown to emerge systematically as particular cases of our formalism. As examples of new possibilities, the case of accelerated observers and that of cosmic string backgrounds are presented.
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    Exact solution of the n-dimensional Dirac–Coulomb equation (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1677-1680 
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    Notes: An exact solution of the n-dimensional Dirac–Coulomb equation is obtained with the radial wave function containing only one term of a confluent hypergeometric function. It is of the same form as the solutions to the Schrödinger and Klein–Gordon equations with a Coulomb potential in n dimensions.
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    Refined asymptotic expansion for the partition function of unbounded quantum billiards (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1670-1676 
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    Notes: This paper presents a refined asymptotic expansion for the partition function aitch-theta(t)=Tr etΔ of quantum billiards in the unbounded regions {0≤x,0≤yxμ≤1}, μ〉0, and {0≤ye||x||≤1}⊆R2, where Δ is the Dirichlet Laplacian. Simon [Ann. Phys. 146, 209 (1983); J. Funct. Anal. 53, 84 (1983)] determined the leading divergence of the trace of the heat kernel for the first class of systems. Standard techniques are combined for the evaluation of aitch-theta for bounded region billiards with results by Van den Berg [J. Funct. Anal. 71, 279 (1987)] for "horn-shaped regions'' using an optimized way of dividing the region into "narrow'' and "wide'' parts to determine the first three terms in the asymptotic expansion of aitch-theta. Results are also stated for bounded regions with cusps that can be obtained by the same method. As an application, the spectral staircase of the strongly chaotic billiard system defined in the region {0≤xy≤2,x≥0}, which has been discussed in connection with the Riemann ζ function and the search for quantum chaos is considered.
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    Low-frequency moments in inverse scattering theory (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1691-1692 
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    Notes: The low-frequency moments of the scattering amplitude are utilized in order to identify the capacity, the center, and the orientation of an acoustically soft scatterer.
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    Extended Hilbert space approach to few-body problems (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1681-1690 
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    Notes: A general formulation of the quantum scattering theory for a system of few particles, which have an internal structure, is given. Due to freezing out the internal degrees of freedom in the external channels, a certain class of energy-dependent potentials is generated. By means of potential theory, a modified Faddeev equation is derived both in external and internal channels. The Fredholmity of these equations is proven and this is what provides a sound basis for solving the addressed scattering problem.
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    Summational invariants in systems of mass points and rigid bodies (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1693-1697 
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    Topics: Mathematics , Physics
    Notes: For systems of rigid bodies and mass points, the general form of summational invariants will be derived using some results of Amigó and Reeh [J. Math. Phys. 24, 1594 (1983)].
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    The linearized gauge field propagator in an inhomogeneous medium (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1661-1669 
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    Notes: In an inhomogeneous medium with μ=κ−1, the linearized gauge field propagator is presented in terms of spherical harmonics for the Coulomb gauge. Explicit expressions for the propagator are given in the case of the MIT bag for both the Coulomb and Lorentz gauges. Gauge invariance is shown explicitly for the one gluon interaction in the MIT bag. This work supplements and corrects the earlier work by Bickeböller, Goldflam, and Wilets [J. Math. Phys. 26, 1810 (1985)].
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    Conformally Ricci-flat viscous fluids (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1704-1706 
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    Notes: It is shown that if the gradient of the conformal scalar in a conformally Ricci-flat space-time is parallel to an eigenvector (timelike, spacelike, or null) of the stress-energy tensor, then acceptable solutions, without restrictions on the physical and kinematical quantities, of the Einstein field equations for a viscous fluid with heat conduction may be found.
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    Equations of state and plane-autonomous systems in Bianchi V imperfect fluid cosmology (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1698-1703 
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    Notes: A new general approach for investigating imperfect fluid cosmological models is introduced in which the equations of state are completely "dimensionless.'' Such equations of state are then utilized to reduce the Einstein field equations governing Bianchi V imperfect fluid cosmologies to a plane-autonomous system of equations, thus enabling the qualitative behavior of these cosmological models to be analyzed in a straightforward manner. The resulting plane-autonomous system is investigated. Finally, exact solutions of the Bianchi V imperfect fluid field equations in the case when the equations of state take on a particularly simple form are discussed.
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    The covariant linear oscillator and generalized realization of the dynamical SU(1,1) symmetry algebra (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1733-1738 
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    Notes: An exactly solvable problem for the finite-difference Schrödinger equation in the relativistic configurational space is considered. The appropriate finite-difference generalization of the factorization method is developed. The theory of new special functions "the relativistic Hermite polynomials,'' in which the solutions are expressed, is constructed.
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    Transversal affine connection and quantization of constrained systems (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1723-1732 
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    Notes: The Dirac quantization of a finite-dimensional relativistic system with a quadratic super-Hamiltonian and linear supermomenta is investigated. In a previous work, the operator constraints were consistently factor-ordered in such a way that the resulting quantum theory was invariant under all relevant transformations of the classical theory. The method was based on a special choice of coordinates and gauge. Here, coordinate-independent methods are worked out and a quite general gauge is used. A new mathematical concept, the so-called "transversal affine connection,'' is introduced. This connection is not a linear connection and is associated with a degenerate metric. The corresponding curvature tensor is defined and its components are calculated. The formalism is used to reconstruct the operator constraints, clarify their geometric meaning, and calculate their commutators.
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    Introduction to a covariant theory of special functions of mathematical physics (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2840-2850 
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    Notes: Using harmonic analysis techniquies, the covariant expression of Jacobi and Hermite polynomials on an n-dimensional space endowed with a metric g of signature (p+, q−) is given. The properties of these polynomials are studied and their relations with the hypergeometric function are given.
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    Integrable Hamiltonian systems related to the polynomial eigenvalue problem (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2835-2839 
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    Notes: The independent integrals of motion in involution for the Hamiltonian system related to the second-order polynomial eigenvalue problem are constructed by using relevant recursion formula. The hierarchy of Hamiltonian systems obtained from the above problem and the time part of the Lax pair are shown to be completely integrable and they are shown to commute with each other. Furthermore, their solution solves the evolution equation associated with the Lax pair.
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    Complete integrability and analytic solutions of a KdV-type equation (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2851-2855 
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    Notes: The complete integrability of the variable coefficient version of a KdV equation via the Painlevé approach is analyzed. Through the Painlevé–Bäcklund equations, its auto-Bäcklund transformation, Lax pairs, symmetry, strong symmetry, bilinear form, and analytic solutions are obtained.
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    Lie algebraic methods and solutions of linear partial differential equations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2856-2863 
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    Notes: In this paper, an algebraic method to obtain the solution of linear partial differential equations of the evolution type is discussed. The proposed method exploits the Lie differential operators and their matrix realization, to reduce the equation to an easily solvable generalized matrix form. Some applications to problems of specific interest are also discussed.
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    A geometric approach to the path integral formalism of p-branes (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2864-2871 
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    Notes: The configuration space for a path integral description of a p-brane is seen as a vector bundle over moduli spaces. The Einstein condition, applied to such vector bundles over compact Kähler manifolds, provides the required stability conditions. Consequently moduli spaces for such extended objects of higher dimensionality are constructed. Finally a Hermitian metric can be introduced in these moduli spaces.
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    Bäcklund transformations for surfaces in Minkowski space (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2872-2875 
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    Notes: A Bäcklund transformation is constructed between spacelike surfaces of constant negative curvature and timelike surfaces of constant negative curvature in three-dimensional Minkowksi space. The transformation gives a differential geometric interpretation to a Bäcklund transformation between the elliptic sine-Gordon equation and the elliptic sinh-Gordon equation studied by Leibbrandt [J. Math. Phys. 19, (1978)].
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    Some symmetries of quantum dimensions (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1770-1775 
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    Notes: Several useful properties of the quantum dimensions of representations of Uq(sl(n)) for q a root of unity are established. The results can be used to calculate truncated Kronecker products of these representations and hence to investigate the isomorphism between these truncated tensor products and the fusion rules of the WZW theories associated with Uq(sl(n)).
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    Unified models from gauged supergroups. I. Dimensional reduction formalism. Unitary and orthosymplectic series (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1783-1790 
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    Notes: Principles are elaborated for constructing consistent grand unified models (GUT's) plus Higgs sectors from dimensional reduction of gauged supergroups over graded coset spaces. A search of possible GUT groups is made for unitary and orthosymplectic supergroups over a space parametrized by a single pair of Grassmann coordinates.
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    Trapped surfaces in monopole-like Cauchy data of Einstein–Yang–Mills–Higgs equations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1791-1795 
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    Notes: The non-Abelian monopole solution of Bogomolny, Prasad, and Sommerfield is chosen as a part of the Cauchy data for the evolution of Einstein–Yang–Mills–Higgs equations. Momentarily static spherically symmetric data for gravitational fields are obtained numerically via the Lichnerowicz equation. In the case of generic scaling of fields initial data with trapped surfaces were found.
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    On an exceptional nonassociative superspace (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1776-1782 
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    Notes: The Jordan superalgebra JF(6/4) is the unique exceptional Jordan superalgebra that has no realization in terms of Z2-graded associative supermatrices. It is proposed to be the basis of an exceptional superspace that is non-Clifford algebraic. The JF(6/4) is constructed in a basis that renders itself to such an interpretation and its derivation, reduced structure, and Möbius superalgebras are studied. These algebras are simply the Lie superalgebras of generalized rotation, the Lorentz group, and conformal supergroup of the Jordan superalgebra JF(6/4). We also comment on the implications of the exceptionality of JF(6/4).
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    Wave functions of bound states of a fermion and a Dirac dyon and matrix elements in an external electromagnetic field (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1796-1799 
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    Notes: Wave functions of bound states for a fermion and a Dirac dyon with charge Zd〈Zcd and for j≥||q||+ 1/2 are obtained. Matrix elements of this system in the external electromagnetic field are calculated and the corresponding selection rules are shown.
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    Minimization of Landau potentials invariant under O(3).II (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1300-1303 
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    Notes: In a previous paper, the absolute minima for Landau potentials were computed for the irreducible representations of SO(3) or O(3) of spin up to four. Here, this analysis is extended to the case of spin five and six. Some novel properties of the extrema are pointed out.
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    Similarity transformations of irreducible corepresentations in Wigner canonical form (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1304-1309 
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    Notes: The general form of the matrices that transform an irreducible corepresentation (coirrep) into an equivalent one, where both representations are assumed to be in the form proposed by Wigner, is analyzed for the three types of coirreps. In addition, the relation of these transformations to inner automorphisms of the corresponding group algebras is clarified.
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    Beyond Gaussian integrals in Grassman algebra (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1297-1299 
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    Notes: Using the properties of determinants, the exact expressions for integrals of functions of the type exp[ηAη¯+(ηBη¯)l] and their moments, where η and η¯ are Grassman generators with N components are derived.
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    Finite geometries and Clifford algebras. II (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1315-1324 
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    Notes: The Clifford algebra in dimension d=2m+1−1, m≥2, is treated using the finite m-dimensional projective geometry PG(m, 2) over the field of order 2. Full details are given for the case m=4, d=31, generalizing previous work for m=2 and 3. Details are given of some configurations that arise in PG(4, 2).
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    Shifted tableaux, Schur's Q functions, and Kronecker products of Sn spin irreps (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1310-1314 
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    Notes: Properties of shifted tableaux have been explored in order to improve the algorithm for the calculation of Q function outer products. A simple technique has been established for finding out the highest and lowest partitions in the expansion of Q function outer products. Using these techniques and Young's raising operators, we have completed the Kronecker product for Sn spin irreps.
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    Explicit orthonormal Clebsch–Gordan coefficients of SU(3) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1325-1332 
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    Notes: The construction of the explicit algebraic-polynomial expressions for the nonmultiplicity-free orthonormal Clebsch–Gordan (Wigner) coefficients of SU(3)&supuline;U(2) is completed in the case of the paracanonical coupling scheme related with the explicit minimal biorthogonal systems by means of the Hecht or Gram–Schmidt process. The direct and inverse orthogonalization coefficients (the first of them being equivalent to the boundary orthonormal isofactors) are expressed, up to explicitly given multiplicative factors, in terms of the numerator and denominator polynomials related with the auxiliary Aλ function of Louck, Biedenharn, and Lohe that appears as a fragment of the denominator G-functions of canonical SU(3) tensor operators.
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    Semiclassical structure of trace formulas (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2952-2977 
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    Notes: Trace formulas provide the only general relations known connecting quantum mechanics with classical mechanics in the case that the classical motion is chaotic. In particular, they connect quantal objects such as the density of states with classical periodic orbits. In this paper, several trace formulas, including those of Gutzwiller, Balian and Bloch, Tabor, and Berry, are examined from a geometrical standpoint. New forms of the amplitude determinant in asymptotic theory are developed as tools for this examination. The meaning of caustics in these formulas is revealed in terms of intersections of Lagrangian manifolds in phase space. The periodic orbits themselves appear as caustics of an unstable kind, lying on the intersection of two Lagrangian manifolds in the appropriate phase space. New insight is obtained into the Weyl correspondence and the Wigner function, especially their caustic structures.
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    On the structure of quantum phase space (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2987-2995 
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    Notes: The space of labels characterizing the elements of Schwinger's basis for unitary quantum operators is endowed with a structure of symplectic type. This structure is embodied in a certain algebraic cocycle, whose main features are inherited by the symplectic form of classical phase space. In consequence, the label space may be taken as the quantum phase space: It plays, in the quantum case, the same role played by phase space in classical mechanics, some differences coming inevitably from its nonlinear character.
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    On the linearization stability of the conformally (anti-) self-dual Einstein equations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2983-2986 
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    Notes: The Einstein equations with a cosmological constant, when restricted to Euclidean space-times with anti-self-dual Weyl tensor, can be replaced by a quadratic condition on the curvature of an SU(2) (spin) connection. As has been shown elsewhere, when the cosmological constant is positive and the space-time is compact, the moduli space of gauge-inequivalent solutions to this equation is discrete, i.e., zero dimensional; when the cosmological constant is negative, the dimension of the moduli space is essentially controlled by the Atiyah–Singer index theorem provided the field equations are linearization stable. It is shown that linearization instability occurs whenever the unperturbed geometry possesses a Killing vector and/or a "harmonic Weyl spinor.'' It is then proven that while there are no Killing vectors on compact conformally anti-self-dual Einstein spaces with a negative cosmological constant, it is possible to have harmonic Weyl spinors. Therefore, the conformally anti-self-dual Einstein equations on a compact Euclidean manifold are linearization stable when the cosmological constant is negative provided the unperturbed geometry admits no harmonic Weyl spinors.
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    How solvable is (2+1)-dimensional Einstein gravity? (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2978-2982 
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    Notes: In this paper, the relationship between Witten's approach to the (2+1)-dimensional, vacuum Einstein equations (for spatially compact space-times) and the conventional Annowitt, Deser, and Misner (ADM) Hamiltonian approach is discussed. It is argued (especially for the space-times with higher genus Cauchy surfaces) that neither approach is complete in itself; Witten's because it does not provide a technique (even at the classical level) for recovering the space-time metric and the conventional approach because it provides no mechanism for solving a seemingly intractable set of Hamilton equations. It is also argued, however, that the two formulations are instead complementary in the sense that the Wilson loops, which play a key role in Witten's approach, provide (at least in principle) a mechanism for solving the reduced Hamilton equations and thereby completing the picture at the classical level. An example of this synthesis for the (explicitly computable) case of genus-one hypersurfaces is provided. The more tenuous problem of whether this synthesis can be extended to the quantized Einstein equations will also be discussed. A principal open question is whether the Wilson loops, when expressed in terms of the ADM canonical variables, can be ordered in such a way as to preserve, quantum mechanically, their (classical) Poisson bracket algebra.
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    Completely solvable models of the nonlinear Boltzmann equation I. Case of three velocities (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 3003-3029 
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    Notes: In one space and one time dimension, a class of models of the nonlinear Boltzmann equation is presented that is exactly solvable for all initial conditions. The models have three velocity components and the following desirable properties: (a) conservation of the number of particles; (b) energy conservation; (c) nonlinearity; (d) positivity of distribution functions; and (e) unique equilibrium state (for any given density), which is approached as t→∞. These models are very rich in structure, and some of their simple properties are studied.
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    The Goursat problem for Maxwell's equations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 3085-3088 
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    Notes: Using the spinor formalism of electromagnetism, the Goursat problem for Maxell's equations is defined and some examples of solutions are given.
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    New link polynomial obtained from octet representation of quantum sl (3) enveloping algebra (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 3079-3084 
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    Notes: The quantum Clebsch–Gordan coefficients for the coproduct 8×8 of the quantum sl(3) enveloping algebra are computed. In the decomposition of the coproduct 8×8, there are two octet representations that are identified by the symmetry in changing the order of the factor octet representations. The corresponding Rq matrix and a new link polynomial are obtained.
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    Three-dimensional quantum groups from contractions of SU(2)q (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2548-2551 
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    Notes: Contractions of Lie algebras and of their representations are generalized to define new quantum groups. An explicit and complete exposition is made for the one-dimensional Heisenberg H(1)q and the two-dimensional Euclidean quantum group E(2)q obtained by contracting SU(2)q.
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    Beltrami algebra and symmetry of the Beltrami equation on Riemann surfaces (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2543-2547 
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    Notes: It is shown that the Beltrami equation has an infinite-dimensional symmetry, namely the Beltrami algebra, on its solution spaces. The Beltrami algebra with central extension and its supersymmetric version are explicitly found.
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    Automorphisms and general charge conjugations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2560-2566 
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    Notes: It is shown how outer automorphisms of a semisimple Lie algebra and automorphisms of the corresponding root system describe conjugations of general charges. New results about representations of semidirect products of non-Abelian Lie groups and about projective representations of finite groups are derived.
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    A parametrization for independent variables of a two-matrix hypergeometric function (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2570-2571 
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    Notes: A new parametrization for the independent variables of the two-matrix hypergeometric function 0F(k)0(a,b) is given. This parametrization results in a net reduction of two variables. The new arguments for the zonal polynomials in the series representation of 0F(k)0(a,b), multiplied by an exponential factor, are all in the interval [0,1], which greatly improves the convergence of the series. The results are of practical use in a number of applications, such as the configuration statistics of macromolecules, shapes of random walks, and multivariate statistics.
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    On a Fourier integral over SO(3) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2567-2569 
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    Notes: A two-matrix function of general interest in the areas of configuration statistics of macromolecules, number theory, harmonic analysis, and multivariate statistics is studied. The function is defined as a Fourier integral over SO(3), the Lie group of orthogonal 3×3 matrices with unit determinant. This six-variable function is first expressed as a product of a three-variable function and an exponential function of an additional variable, thereby reducing the total number of independent variables by 2. The new function with three parameters is expressible either as a double integral or as a series in one of the variables with the coefficients being polynomials in the other two. A special, nontrivial case where one of three arguments of the function takes a particular value is explored thoroughly. The resulting two-variable function is real valued and is an oscillating function of one of the variables when the other is fixed. When this function is expanded as a power series in one of the two variables, it generates polynomials in the other variable. Numerical analysis of this series shows it to be rapidly convergent and it is of practical use in the numerical evaluation of the function. Although the connection between these newly found polynomials and zonal polynomials has not been investigated, the parametrization for the four new variables of the two-matrix function studied may well prove useful in the effective numerical evaluation of the function when expressed alternatively as a series in zonal polynomials with an exponential part factored out.
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    A search for integrable bilinear equations: The Painlevé approach (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2572-2578 
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    Notes: The possibility of the existence of new integrable partial differential equations is investigated, the tools of singularity analysis. The equations treated are written in the Hirota bilinear formalism. It is shown here how to apply the Painlevé method directly under the bilinear form. Just by studying the dominant part of the equations, the number of cases to be considered can be limited drastically. Finally, the partial differential equations identified in a previous work [J. Hietarinta, J. Meth. Phys. 28, 1732, 2096, and 2586 (1987); 29, 628 (1988)] as possessing at least four soliton solutions, are shown to pass the Painlevé test as well, which is a strong indication of their integrability.
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    Rotations, squeezing, and the unitary transformation operator from individual particles to Jacobi variables (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1413-1415 
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    Notes: A unitary operator for the transformation from individual particles to Jacobi variables is constructed explicitly for particles of arbitrary masses. It is expressed as a product of rotation and squeezing operators using only canonical variables.
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    The asymptotic localization of position probability in quantum mechanics (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1435-1440 
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    Notes: The method of stationary phase is discussed in a mathematically rigorous way. A resulting lemma is used to derive the asymptotic localization of position probability under the evolution operator Ut=F−1 exp(−iωt)F, where ω is a continuous function of the wave vector k=(k1,...,kN) (N=1,2,...) with continuous first and second derivatives. The measurement of velocity is discussed, and the interpretation of the self-adjoint operator vˆi=F−1∇iωF as representing the ith component of velocity is also discussed.
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    The one-dimensional Coulomb potential as a generalized function and the hidden O(2) symmetry (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1441-1444 
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    Notes: The one-dimensional hydrogen atom treating the potential, –λ /||x||, is solved as a generalized function. The solutions (although nondegenerate) are nonunique unless fixed by some physical constraint. It is also shown that the hidden O(2) symmetry is a consequence of using solutions that are eigenfunctions of the operator sgn x≡x/||x||.
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    Conserved quantities and symmetries of KP hierarchy (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1426-1434 
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    Notes: Conserved quantities and symmetries of the KP equation from the point of view of the Sato theory that provides a unifying approach to soliton equations is studied. Conserved quantities are derived from the generalized Lax equations. Some reductions of the KP hierarchy such as KdV, Boussinesq, a coupled KdV, and Sawada–Kotera equation are also considered. By expansion of the squared eigenfunctions of the Lax equations in terms of the τ function, symmetries of the KP equations are obtained. The relationship of this procedure to the two-dimensional recursion operator newly found by Fokas and Santini is discussed.
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    Killing vectors of static spherically symmetric metrics (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1463-1463 
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    Notes: An error in a previous theorem [J. Math. Phys. 28, 1019 (1987); 29, 525 (1988)] is corrected and the theorem is extended.
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    Anisotropic cosmological models with energy density dependent bulk viscosity (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1456-1462 
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    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An analysis is presented of the Bianchi type I cosmological models with a bulk viscosity when the universe is filled with the stiff fluid p=ε while the viscosity is a power function of the energy density, such as η=α||ε||n. Although the exact solutions are obtainable only when the 2n is an integer, the characteristics of evolution can be clarified for the models with arbitrary value of n. It is shown that, except for the n=0 model that has solutions with infinite energy density at initial state, the anisotropic solutions that evolve to positive Hubble functions in the later stage will begin with Kasner-type curvature singularity and zero energy density at finite past for the n≥1 models, and with finite Hubble functions and finite negative energy density at infinite past for the n〈1 models. In the course of evolution, matters are created and the anisotropies of the universe are smoothed out. At the final stage, cosmologies are driven to infinite expansion state, de Sitter space-time, or Friedman universe asymptotically. However, the de Sitter space-time is the only attractor state for the n〈 (1)/(2) models. The solutions that are free of cosmological singularity for any finite proper time are singled out. The extension to the higher-dimensional models is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528736
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    The Dirac equation in a non-Riemannian manifold: II. An analysis using an internal local n-dimensional space of the Yang–Mills type (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1478-1482 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The geometrical properties of a flat tangent space-time local to the generalized manifold of the Einstein–Schrödinger nonsymmetric theory, with an internal n-dimensional space with the SU(n) symmetry group, is developed here. As an application of the theory, a generalized Dirac equation, where the electromagnetic and the Yang–Mills fields are included in a more complex field equation, is then obtained. When the two-dimensional case is considered, the theory can be immediately interpreted through the algebra of quaternions, which, through the Hurwitz theorem, presupposes a generalization of the theory using the algebra of octonions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528740
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    Quantum mechanics with higher time derivatives: Some mathematical facts and the inclusion of gravitational self-interaction (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2637-2652 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The inclusion of self-interaction, in particular, gravitational into the quantum mechanics of a particle (first quantization) implies two necessary features: dealing with quantum mechanics involving the second time derivative and the construction of a variational principle maintaining the rescaling invariance of the wave function. The relevant variational principle is constructed which is not the principle of extremality of any action. Some general mathematical facts lain in the basis of this construction are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528965
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    Star quantization on the cylinder (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2672-2682 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Star-product quantization as an autonomous quantum theory is reviewed with emphasis on its relation to path integral and Hilbert space formulations. Quantization of the usual Heisenberg group is used as an example. When phase space is the cylinder, this group is replaced by E(2), the Euclidean group in two dimensions. This case is worked out in detail. In doing so, polarizations on the cylinder are discussed and a phase space path integral is constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528968
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    Effective actions with vector-axial-vector couplings on Riemann–Cartan manifolds (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2699-2701 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The general forms of quantum effective actions in the presence of vector and axial-vector gauge potentials on Riemann–Cartan manifolds with torsion are discussed. The relations between different forms of anomalies are elucidated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529033
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    Gauge field systems on CPn (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1506-1512 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: SU(n)×U(1) gauge fields on CPn are constructed in a gauge where the connection is expressed in so(n−1). The (anti)self-duality relations satisfied by these fields are given, and the 2n-dimensional gauge field systems whose Bogomolnyi bounds are saturated by these are discussed. Other gauge field systems, not endowed with topological lower bounds, are also discussed. The analogy between all these gauge field systems on CPn and S2n is highlighted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528693
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    Addendum to "The equivariant inverse problem in gauge field theories and the uniqueness of the Yang–Mills equations'' [J. Math. Phys. 30, 2382 (1989)] (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1503-1503 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The main theorem of the previous paper is extended to the case where L=L(gi j ; Aαi; Aαi,j). References and notations are the same.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528743
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    Separation of variables and exact solution to the Dirac equation in curvilinear orthogonal coordinates with cylindrical symmetry (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2702-2707 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In the present article, a complete separation of variables in the Dirac equation for a free particle is achieved in parabolic cylinder and elliptical coordinates. The resulting system of ordinary differential equations is solved and the asymptotic behavior of the spinor solution is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528972
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    Parastatistics, supersymmetry and parasupercoherent states (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1513-1523 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Coherent states are constructed in p=2-parasupersymmetric quantum mechanics in connection with the two relative para-Bose and para-Fermi sets of trilinear structure relations. They are called parasupercoherent states. Parasupersymmetric operators [such as the Hamiltonian and (two) annihilation operators] are introduced and discussed. In particular, the parasuperspectrum is determined and compared with the recent results obtained by Rubakov and Spiridonov [Mod. Phys. Lett. A 3, 1337 (1988)]. The superalgebra contents subtended by osp(2/2) and osp(3/2) are analyzed and exploited in order to get constants of motion in both contexts through parallel properties on the supersymmetric harmonic oscillator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528694
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    Classification of all star and grade star irreps of gl(n||1) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1524-1534 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A method for inducing nondegenerate forms on irreducible gl(m||n) modules that implies some general results on star and grade star representations is investigated. These results are applied to obtain a complete classification, in terms of highest weights, of the irreducible star and grade star representations of gl(n||1). It is demonstrated that while gl(n||1) admits a large class of star representations the irreducible grade star representations are comparatively rare. Moreover, for n≠2 all grade star irreducible representations are also star representations and, for n〉2, are atypical. The superalgebra gl(2||1) proves to be a special case and admits a two-parameter family of four-dimensional typical grade star irreducible representations that are not star representations. In particular, typical grade star irreducible representations of gl(n||1) exist only for n=1,2.
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    URL: http://dx.doi.org/10.1063/1.528695
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    On the complete system of observables in quantum mechanics (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2406-2409 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper contains a series of remarks about the concept of Complete System of Observables (CSO) in quantum mechanics and a discussion of two definitions of CSO, one given by Jauch [Helv. Phys. Acta 33, 711 (1960)] and the other by Prugovecki [Can. J. Phys. 47, 1083 (1968)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528844
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    Infinite-dimensional algebras and a trigonometric basis for the classical Lie algebras (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1088-1094 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper explores features of the infinite-dimensional algebras that have been previously introduced. In particular, it is shown that the classical simple Lie algebras (AN, BN, CN, DN) may be expressed in an "egalitarian'' basis with trigonometric structure constants. The transformation to the standard Cartan–Weyl basis, and the particularly transparent N→∞ limit that this formulation allows is provided.
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    URL: http://dx.doi.org/10.1063/1.528788
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    Nonlinear equations invariant under the Poincaré, similitude, and conformal groups in two-dimensional space-time (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1095-1105 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: All realizations of the Lie algebras p(1,1), sim(1,1), and conf(1,1) are classified under the action of the group of local diffeomorphisms of R3. The result is used to obtain all second-order scalar differential equations, invariant under the corresponding Poincaré, similitude, and conformal groups. The invariant equations are, in general, nonlinear, and the requirement of linearity turns out to be very restrictive. Group invariant solutions of some of the conformally invariant equations are obtained either by quadratures or by a linearizing transformation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528789
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    Nonspurious harmonic oscillator states in single particle coordinates (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1164-1166 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A procedure for the construction of nonspurious harmonic oscillator wave functions with arbitrary permutational symmetry has recently been proposed. The resulting wave functions are expressed in terms of normalized Jacobi coordinates, and involve a new type of harmonic oscillator coefficients of fractional parentage. A simple algorithm to transform these states from the Jacobi coordinates to the single particle coordinates is presented. This is a generalization to an arbitrary number of particles of the harmonic oscillator transformation from center-of-mass and relative coordinates to single particle coordinates.
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    URL: http://dx.doi.org/10.1063/1.528747
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