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  • Articles  (3,913)
  • American Chemical Society  (3,439)
  • American Institute of Physics (AIP)  (474)
  • 1990-1994  (3,913)
  • 1992  (3,913)
  • Biology  (3,439)
  • Mathematics  (474)
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  • Articles  (3,913)
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  • 1990-1994  (3,913)
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  • 1
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    General method for reducing the two-body Dirac equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2618-2625 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A semirelativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schrödinger-type equations is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529978
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  • 2
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    Singularities in the solutions of the massive Skyrme model (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2626-2632 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The equation of motion for the Skyrme model with a pion mass term is studied in the framework of the Painlevé analysis, and information is obtained about the singularity structure of its solutions. As in the massless case, singularities exist, consisting of a first-order pole term superposed to a logarithmic branch point. For the solitonic solutions, the singularities form an infinite sequence of points located on the negative real axis of the squared radial variable, accumulating at the origin. Based on this property and on the asymptotic behavior of the solitonic solutions, an approximate representation is built for the baryonic soliton, which is extremely accurate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529581
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  • 3
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    Weyl manifolds and connections (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2633-2638 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A study is made of Weyl connections and their associated holonomy groups. The extent to which a Weyl connection determines its associated metric and 1-form structures is also discussed. Finally, the related concept of a locally metric connection is introduced and some relations between metric, locally metric, and Weyl connections are established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529582
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  • 4
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    Asymptotically exact diffusive boundary conditions in linear kinetic theory (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2639-2647 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In a recent article in this journal, asymptotic considerations were used to define appropriate boundary conditions for diffusive approximations to linear kinetic equations. A variational treatment was invoked to carry out the details of the analysis. Here these details are carried out exactly, and it is shown that the earlier variational results are accurate to a few percent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529583
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  • 5
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    Representations of the quantum algebras Uq(ur,s) and Uq(ur+s) related to the quantum hyperboloid and sphere (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1937-1947 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Representations πΛμ of the principal degenerate series of the quantum algebra Uq(ur,s) are introduced. Structure of these representations is studied. Several classes of unitary irreducible representations of the algebra Uq(ur,s) are separated in the set of irreducible representations πΛμ and irreducible constituents of reducible representations πΛμ. The formulas of action of operators of irreducible representations of the quantum algebra Uq(ur+s) in the basis corresponding to restriction of representations onto the subalgebra Uq(ur+us) are given.
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    URL: http://dx.doi.org/10.1063/1.529669
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  • 6
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    Computation of error effects in nonlinear Hamiltonian systems using Lie algebraic methods (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1948-1963 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: There exist Lie algebraic methods for obtaining transfer maps around any given trajectory of a Hamiltonian system. This paper describes an iterative procedure for finding transfer maps around the same trajectory when the Hamiltonian is perturbed by small linear terms. Such terms often result when an actual system deviates from an ideal one due to errors. Two examples from accelerator physics are worked out. Comparisons with numerical computations, and in simple cases exact analytical calculations, demonstrate the validity of the procedure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529670
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  • 7
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    Universal L operator and invariants of the quantum supergroup Uq(gl(m/n)) (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1970-1979 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A spectral parameter-dependent solution of the graded Yang–Baxter equation is obtained, which is universal in the sense that it lives in Uq(gl(m/n))⊗End(V) with V the vector module of Uq(gl(m/n)). The invariants of this quantum supergroup are constructed using this solution.
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    URL: http://dx.doi.org/10.1063/1.529672
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  • 8
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    Casimir operators, duality, and the point groups (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1964-1969 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In atomic or nuclear shell theory the quadratic Casimir operators can be used to evaluate the expectation values of two-body interactions among equivalent members of a shell. Racah has given closed expressions for these Casimir operators for all the groups in the Racah chain. In this paper an alternate derivation of these closed expressions based on duality with the symmetric group is given. The derivation allows extension of these expressions to situations in which equivalent spins are in an environment, such as a point group, for which the two-body interactions separate into distinct sets. Possible application to NMR systems with spin ≥1/2 are discussed.
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    URL: http://dx.doi.org/10.1063/1.529671
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  • 9
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    Comment on "The matrix representation of U4 in the U2×U2 basis and isoscalar factors for Up+q&supuline;Up×Uq'' [F. Pan, J. Math. Phys. 31, 1333 (1990)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1980-1982 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Complementary group technique leads to more simple solutions of some problems considered by F. Pan [J. Math. Phys. 31, 1333 (1990)], including special resubducing coefficients and isoscalar factors of unitary groups.
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    URL: http://dx.doi.org/10.1063/1.529673
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  • 10
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    Explicit canonical tensor operators and orthonormal coupling coefficients of SU(3) (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1983-2004 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The canonical unit SU(3) tensor operators are constructed by means of the stretched coupling of the auxiliary maximal and minimal null space tensor operators, with the renormalization factors expressed in terms of the denominator functions of Biedenharn, Gustafson, Lohe, Louck, and Milne. The matrix elements of the maximal null space tensor operators are expressed with the help of the modified projection operators of Asherova and Smirnov. The self-conjugate minimal null space tensor operators are expressed in terms of the group generators with the help of the weight lowering operator technique. The corresponding extreme isoscalar factors of the Clebsch–Gordan (Wigner) coefficients are used as constructive elements of the explicit recursive expression for the general orthonormal isoscalar factors of SU(3) with its considerable simplication for the boundary values of parameters. The general isofactors are also expanded in the different ways in terms of their boundary values. The new classes of the generalized hypergeometric series are used as constructive elements of the SU(3) and SU(2) representation theory functions and their properties are considered.
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    URL: http://dx.doi.org/10.1063/1.529622
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  • 11
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    Cauchy problem for the linearized version of the Generalized Polynomial KdV equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2013-2022 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In the present paper results about the "Generalized Polynomial Korteweg–de Vries equation'' (GPKdV) are obtained, extending the ones by Sachs [SIAM J. Math. Anal. 14, 674 (1983)] for the Korteweg–de Vries (KdV) equation. Namely, the evolution of the so-called "prolonged squared'' eigenfunctions of the associated spectral problem according to the linearized GPKdV is proven, the Lax pairs associated with the "prolonged'' eigenfunctions as well as "prolonged squared'' eigenfunctions are derived, and on the basis of some expansion formulas the Cauchy problem for the linearized GPKdV with a decreasing at infinity initial condition is solved.
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    URL: http://dx.doi.org/10.1063/1.529624
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  • 12
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    Evaluation of the spherical Bessel transform of a Whittaker function: An application of a difference equation method (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2005-2012 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple analytic expression for the spherical Bessel transform of the zero-range bound state wave function with the Coulomb interaction present, for the lth partial wave, expressed as a Whittaker function, is obtained. The result is given in terms of polynomials of degree l, the exponential function, and a simple hypergeometric function which is independent of l. Transformations of this latter function are derived in terms of more rapidly convergent series. The method presented has much wider application, since it relies essentially only on the existence of differential-difference equations for the functions involved, and the solution of the inhomogeneous difference and differential equations satisfied by the transform.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529623
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  • 13
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    A first integral for a class of time-dependent anharmonic oscillators with multiple anharmonicities (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2023-2030 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The integrability of the equation q¨=f(t)q2+g(t)q3+h(t)q4+j(t)q5 is considered. Particular cases of this equation arise in the study of charged plasma in an axially symmetric magnetic field and in shear-free spherically symmetric gravitational fields in general relativity. The above equation with only a quadratic term arises in the study of shear-free fluids, in general [A. Krasinski, J. Math. Phys. 30, 433 (1989)]. The equation with a cubic term is applicable when there is an electromagnetic field. In special cases we reduce the solution to a quadrature that has solutions in terms of elliptic integrals. A Lie point symmetry analysis is performed and the different cases that arise are considered for the existence of a symmetry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529625
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  • 14
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    Schlesinger transformations of Painlevé II-V (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2031-2045 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The explicit form of the Schlesinger transformations for the second, third, fourth, and fifth Painlevé equations is given.
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    URL: http://dx.doi.org/10.1063/1.529626
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  • 15
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    P determinants and boundary values (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2046-2052 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that a regularized determinant based on Hilbert's approach (which we call the "p determinant'') of a quotient of elliptic operators defined on a manifold with boundary is equal to the "p determinant'' of a quotient of pseudodifferential operators. The last ones are entirely expressible in terms of boundary values of solutions of the original differential operators. It is argued that, in the context of quantum field theory, these boundary values also determine the subtractions (i.e., the counterterms) to which this regularization scheme gives rise.
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    URL: http://dx.doi.org/10.1063/1.529627
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  • 16
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    A relation between group- and Cech-cohomology in principal fiber bundles and anomalies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2071-2079 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A natural map between group-cohomology of the structure group of a principal fiber bundle with coefficients in the space of functions from the total space into an Abelian group and Cech-cohomology of the base space is defined. A differential complex of local group-cochains is constructed and an analog of the Poincaré lemma for group-cohomology is proven. By using the machinery of spectral sequences the cohomology of this complex is calculated and the connection between group-cohomology and Cech-cohomology of the given principal fiber bundle is elucidated. Finally, the non-Abelian and Witten anomaly in this context is reviewed and the relevance of our results for lifting principal group actions is discussed.
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    URL: http://dx.doi.org/10.1063/1.529970
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  • 17
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    Quantum quaternions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 171-173 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The notion of quantum quaternions is introduced as a one-parametric quantum deformation of the quaternion algebra. An appriopriate noncommutative differential calculus is developed and the quantum version of the Fueter equation is founded.
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    URL: http://dx.doi.org/10.1063/1.529940
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  • 18
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    Asymmetric anharmonic oscillators in the Hill-determinant picture (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 213-221 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new version of the Hill-determinant construction of bound states is proposed. It is based on the matching of two suitable power-series Ansätze for the wave function. For the asymmetric well potential V(x)=ax+bx2+cx3+dx4 the convergence of the approximants to the physical solutions is proved. For b(approximately-greater-than)bminimal, the Taylor coefficients for this anharmonic oscillator's wave function are specified by four-term recurrences.
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    URL: http://dx.doi.org/10.1063/1.529947
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  • 19
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    Hidden symmetries of two-dimensional systems with local degeneracies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 203-212 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The energy spectrum of a nonrelativistic particle in radial potentials of the form V(r) = αr 2d−2 − βr d−2 shows one level with a singularly high multiplicity. The two-dimensional problems are focused upon and the constants of motion that generate the symmetries responsible for this local accidental degeneracy are determined. The conserved operators realize an SU(2) algebra and the bound states are seen to fall into either finite, semibounded, or unbounded representations of this algebra. An SO(3,2) module encompassing the eigenstates associated to the whole set of potentials is also identified. It is further shown that there exists a second coordinate system besides the polar one in which the Schrödinger equation separates. Finally, it is indicated how the two-dimensional Coulomb and harmonic oscillator problems arise as special cases.
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    URL: http://dx.doi.org/10.1063/1.529946
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  • 20
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    Isometry groups of three-dimensional Riemannian metrics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 267-272 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a group Gr of isometries acting on s-dimensional orbits are given. This provides the list of (abstract) groups that can act isometrically and maximally on such metrics. The conditions are expressed in terms of the eigenvalues and eigenvectors of the Ricci tensor. In any case, the order of differentiability of these data necessary to determine the isometry group is less than 4.
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    URL: http://dx.doi.org/10.1063/1.529960
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  • 21
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    On the instability of the n=1 Einstein–Yang–Mills black holes and mathematically related systems (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 248-255 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The usual approach to analyze the linear stability of a static solution of some system of equations consists of searching for linearized solutions which satisfy suitable boundary conditions spatially and which grow exponentially in time. In the case of the n=1 Einstein–Yang–Mills (EYM) black hole, an interesting situation occurs. There exists a perturbation which grows exponentially in time−and spatially decreases to zero at the horizon−but nevertheless is physically singular on the horizon. Thus, this unstable mode is unacceptable as initial data, and the question arises as to whether the n=1 EYM black hole is stable. We analyze this issue here in the more general case of a scalar field φ satisfying the wave equation ∂2φ/∂t2 = (DaDa − V)φ on a manifold R×M, where Da is the derivative operator associated with a complete Riemannian metric on M and V is a bounded function on M whose derivatives also are bounded. We prove that if the operator A = −DaDa + V fails to be a strictly positive operator on the Hilbert space L2(M), then there exists smooth initial data of compact support in M which give rise to a solution which grows unboundedly with time. This implies that the n=1 EYM black hole and other mathematically similar systems are unstable despite the nonexistence of physically acceptable exponentially growing modes. Rigorous criteria for linear stability are also obtained.
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    URL: http://dx.doi.org/10.1063/1.529957
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  • 22
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    Dirac equation in external fields: Separation of variables in nondiagonal metrics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 297-303 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The algebraic method of separation of variables in the Dirac equation proposed in earlier works by one of the present authors [Theor. Math. Phys. 70, 204 (1987); J. Math. Phys. 30, 2132 (1989)] is developed for the space-time with nondiagonal metrics. The essence of the method consists of the separation of the first-order matricial differential operators that define the dependence of the Dirac's bispinor on the related variables. In contrast to some other authors the pairs of operators are commuted on each step of separation including the variables mixed by nondiagonal elements of fundamental tensor of space-time. There are reasons to believe that it must be some local similarity transformation connected these commuted operators with noncommuted corresponding operators of other authors, although such transformation in view of mathematical difficulties of problem, in general, were not successfully found.
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    URL: http://dx.doi.org/10.1063/1.529964
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  • 23
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    Compact classical systems: so(n) systems (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2126-2137 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Compact quantum systems based on compact kinematical Lie algebras have been described previously [J. Math. Phys. 29, 1521 (1988)]. A "compact classical system'' is obtained as the classical limit of such a compact quantum system. In this paper, compact classical systems obtained in this way from compact quantum systems based on the special orthogonal Lie algebras so(n) are considered; in particular, those based on so(3) and so(4). Such compact classical systems are shown to exhibit behavior strikingly different from that of corresponding noncompact systems in ordinary classical Hamiltonian dynamics.
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    URL: http://dx.doi.org/10.1063/1.529980
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  • 24
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    Integrals, invariant manifolds, and degeneracy for central force problems in Rn (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2138-2147 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Since the notion of angular momentum is defined in any dimension by using the exterior product in Rn, one would guess that central force problems in any dimension are completely integrable, as it is known for n=2 or 3. This is proved explicitly in this paper, by constructing n first integrals independent and involution: the energy and some combinations of the angular momentum components. It is shown that these problems are always reduced to a two-dimensional plane, and the invariant manifolds are topologically, the Cartesian product of those of the reduced problem times n−2 circle factors. It is also proved that for n(approximately-greater-than)2 these problems are degenerate in the sense that their Hamiltonians do not satisfy one of the hypotheses of the Kolmogorov–Arnold–Moser theorem for persistence of invariant tori, when one considers small perturbations.
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    URL: http://dx.doi.org/10.1063/1.529633
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    Existence of gauge field in any partially integrable systems (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2148-2157 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For any integrable and, more generally, any partially integrable model, the existence is shown of a Yang–Mills gauge field with zero curvature, whose gauge group consists of all general coordinate transformations. It has been suggested that this fact may have some connection with existence of an affine connection in the space with zero Riemann curvature tensor. A BRST-like quadratically nilpotent operator is also constructed for any theory with Poisson bracket structure whenever such a connection with zero Riemann curvature exists.
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    URL: http://dx.doi.org/10.1063/1.529634
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  • 26
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    On some mathematical problems in the evaluation of fields produced by currents which are generalized functions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2164-2168 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A method is given to overcome the ambiguities in the order of integration in the calculation of potentials as reciprocal Fourier transform by φ=F˜Fφ=∫dk0∫dk when generalized functions are involved.
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    URL: http://dx.doi.org/10.1063/1.529636
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  • 27
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    Hamiltonization of the Lorentz force equation for a massive particle with spin: A twistorial approach (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2158-2163 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A twistor formulation of the Lorentz force equation is presented. To prepare for its quantization a Poincaré covariant symplectic structure Ω and a Hamiltonian Poincaré scalar function H on T×T (direct product of two twistor spaces less the diagonal, i.e., less the set of points in T×T, where the two twistors coincide), such that the Lorentz force equation for a massive particle with spin corresponds to a (Liouville) flow in T×T generated by H and canonical with respect Ω is introduced.
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    URL: http://dx.doi.org/10.1063/1.529635
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  • 28
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    Real wave equations for positive-frequency electromagnetic fields and their Green's function solutions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2169-2172 
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    Notes: A method is provided whereby solutions of the inhomogeneous wave equations that describe the propagation of positive-frequency photons in the forward tube of complex Minkowski space may be formally expressed in terms of integrals involving the tensor product of appropriate Green's functions. It is pointed out that this method can be used also for treating problems involving wave operators defined on arbitrary product spaces.
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    Bell inequalities on quantum logics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2173-2178 
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    Notes: Three types of Bell inequalities, expressed in terms of quantum logics (orthomodular lattices) and states on them, are studied. It is shown that the two first types are equivalent to the subadditivity of the corresponding state. The third type is equivalent to the existence of a Boolean quotient B of the orthomodular lattice L and a state s¯ on B, such that s¯⋅φ=s, where s is the state on L and φ:L→B is the quotient mapping.
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    Evaluation of the propagator for a quadratic Hamiltonian with arbitrary ordering (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2179-2184 
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    Notes: Path integral methods are used to derive an exact expression for the propagator for a quadratic Hamiltonian with arbitrary ordering. The van Vleck–Pauli relation is found to be a special case of our general result.
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    Supersymmetric extensions of the nonlinear Schrödinger equation: Symmetries and coverings (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2185-2206 
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    Notes: A construction is proposed for a supersymmetric generalization of the cubic Schrödinger equation, resulting in two supersymmetric systems, one of which contains a free parameter. Both systems are proven to admit an infinite set of (higher-order) local and nonlocal symmetries and a seemingly infinite set of conservation laws, the lowest-order terms of which are given explicitly. Moreover, the theory of coverings (equivalent to the prolongation method of Wahlquist and Estabrook) is applied to both systems. Both are seen to admit an infinite-dimensional covering algebra, the structure of which is determined explicitly, resulting in a related supersymmetric system of differential equations, as well as an auto-Bäcklund transformation for each equation. This indicates the complete integrability of both systems.
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    Dirac Hamiltonian with Coulomb potential and spherically symmetric shell contact interactiona) (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2207-2214 
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    Notes: Spherically symmetric Hamiltonians describing a Dirac particle in Coulomb potential combined with contact interaction on a sphere (typically, a δ-shell interaction) are constructed. The point spectrum is studied numerically for the case of scalar and vector δ shells. A comparison of two possible definitions of δ-shell coupling constants is also given.
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    Green functions of the De Rham Laplacian in maximally symmetric spaces (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2228-2231 
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    Notes: The massive p-form two-point functions in maximally symmetric spaces of arbitrary dimension n are obtained.
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    Essential singularities of spherically symmetric space-times (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2262-2264 
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    Notes: The essential singularities of four-dimensional spherically symmetric space-times with some additional symmetries are discussed. The significance of the results is considered.
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    New method of integration for the Dirac equation on a curved space-time (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2279-2289 
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    Notes: A new method of integration of the Dirac equation on curved space-time is presented. The method is based on diagonalization and on separation of variables. The diagonalization allows the use of the well-known method of variables separation of scalar equations for integration of the Dirac equation. All conditions of diagonalization are found. All metrics and potentials admitting the method are presented.
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    Spinor equations in relativistic quantum mechanics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2290-2302 
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    Notes: A set of two first-order equations for classical spinor fields are used to formulate the relativistic quantum mechanics (RQM) of a single massive spin-1/2 particle. These equations are generalized Weyl equations and they are not equivalent to the Dirac equation. They lead to a conserved charge that is not positive definite, thus allowing for a probabilistic interpretation of the wave function in RQM. The charge is also conserved when the fields interact with a scalar field through the charge-current densities.
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    SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. III. Equivalent Lagrangian formalisms (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1571-1578 
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    Notes: The SL(3,R) theory of projective transformations of the plane is applied to the Lagrangians of all one-dimensional Newtonian linear systems. Noether and non-Noether equivalent Lagrangians, as well as the associated Noether and non-Noether constants of motion, are thus obtained in a completely general and systematic way. Complete unification is achieved by this group-theoretic approach to Lagrangians of one-dimensional linear systems.
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    Orbit–orbit branching rules between simple low-rank algebras and equal-rank subalgebras (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1618-1626 
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    Notes: Complete orbit–orbit branching rules, or equivalently, reduction of Weyl group orbits, between each simple algebra of rank 3 or less, and its equal-rank subalgebras and between F4 and each of its equal-rank subalgebras are given. The generic case An&supuline;An−1×U(1), the subjoining F4(approximately-greater-than)B3×U(1), and E8&supuline;E6×A2 (first and seventh highest weight labels nonzero) are also treated. Branching rules between rank 4 and 5 simple algebras and E6 and their equal-rank subalgebras are available in a depository.
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    Realization of the discrete series of unitary representations of Sl(2,R) in terms of creation and annihilation operators (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1627-1630 
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    Notes: A basis for the Hilbert space of the discrete series of unitary representations of Sl(2,R) is constructed as a complete set of coherent states of pairs of particle–antiparticle creation operators. The integer q specifying an irreducible representation is the eigenvalue of the charge operator. Representations with charges (minus-plus)q are equivalent.
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    Graded algebras and geometry based on Yang–Baxter operators (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1631-1635 
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    Notes: The Γ-graded algebras such as the ε-symmetric algebra, generalized Lie algebras and the concept of generalized Lie–Cartan pairs are given in terms of graded Yang–Baxter operators.
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    Analysis on the p-adic superspace. I. Generalized functions: Gaussian distribution (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1636-1642 
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    Notes: The theory of generalized functions on the p-adic superspace Qn,mp over the (super)commutative Banach superalgebra Λ=Λ0⊕Λ1 with the trivial Λ1 annihilator is proposed. The p-adic Gaussian "supermeasure'' is defined as a generalized function on the p-adic superspace. The connection between the p-adic Gaussian integration and the p-adic gamma function of Morita is considered
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    Functional calculus of the Borel transform (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1648-1651 
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    Notes: An explicit form is given of the Borel transform B˜ of g(large-closed-square)f where g(large-closed-square)f(z):=g( f(z)) with f Borel summable and g analytic in f(0) and a detailed study of the singularities in B˜ (in the Borel variable) is made. Examples include g(ξ)=1/ξ, log ξ and eξ. The present paper generalizes results of Boenkost et al. [J. Math. Phys. 29, 1118 (1987)].
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    Jet methods in nonholonomic mechanics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1652-1665 
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    Notes: Classical nonholonomic mechanical systems are studied whose evolution space is a fiber bundle τ: M→R. The framework is that of jet spaces in which the geometrical meaning of the theory emerges clearly. For systems with linear constraints a new interpretation is given of Appell's equations as first-order differential equations associated with a suitable vector field. The d'Alembert principle is formulated in an appropriate way to be generalized to systems with nonlinear constraints. The equivalence between the equations of motion arising from this generalization, the ones set up on Gauss' principle of least constraint and Hertz's principle of least curvature is established.
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    Variational density of electrons for large closed shell atoms (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1672-1674 
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    Notes: An exact expression for the atomic form factor for closed shell atoms is derived using an antisymmetric multielectron wave function. It is shown that for large atoms it can be written as an integral over a Bessel function. Using the Hankel transform it gives an expression for the density of electrons which is of Thomas–Fermi form which was found earlier by Pucci and March.
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    Analysis on the p-adic superspace. II. Differential equations on p-adic superspace (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1643-1647 
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    Notes: The Cauchy problem for differential equations on the p-adic superspace is considered. The application of this mathematical theory to the model of the supersymmetric quantum mechanics on the p-adic Riemannian surface is proposed. The non-Archimedean superdiffusion is also considered.
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    The extension theory and the opening in semitransparent surface (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1685-1689 
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    Notes: The model of zero width slits based on the operator's extension theory for the wave scattering by a semitransparent surface with small aperture is constructed.
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    Super Wigner function (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1690-1694 
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    Notes: The phase-space representation of supersymmetric quantum mechanics is given. The super Wigner function is constructed and its transformation property is investigated. In the case of a supersymmetric oscillator, it is explicitly shown how the invariance under the supersymmetry transformation determines the form of the super Wigner function.
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    Cosmological Yang–Mills hydrodynamics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1782-1785 
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    Notes: The partial differential equations that govern the evolution of a self-gravitating fluid endowed with a density of charge taking its values in a Lie algebra, generating a Yang–Mills current, and hence a Yang–Mills field are written and studied. The local properties of the solutions are analogous to those of gravitating plasmas, but may be quite different globally.
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    A multipolar stationary object embedded in a gravitational field (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1780-1781 
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    Notes: The task of embedding a multipolar stationary object in a gravitational field is undertaken in this paper. It is believed that such an object will be astrophysically interesting.
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    The classical susceptibility and the temperature-dependent susceptibility of a free electron gas (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1799-1806 
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    Notes: The origin of dimensional independence in the classical susceptibility is studied. This study has led to an integral expression for the finite-temperature susceptibility of a free electron gas, given in terms of the zero-temperature susceptibility. At finite temperatures the susceptibility is regular. The singularity, which exists at twice the Fermi wave vector when T=0, vanishes. Thus the anomalous behavior associated with 2kF is expected to disappear when T≠0.
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    Nondispersive solutions of the Klein–Gordon equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1817-1821 
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    Notes: The nondispersive solutions of the Klein–Gordon equation, that is, solutions depending on an arbitrary function F(u), where u is itself a solution of the characteristic equation of the homogeneous three-dimensional scalar wave equation (∇u)2−(c−1∂tu)2=0, are discussed.
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    On a phenomenological generalized Boltzmann equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1786-1798 
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    Notes: In this paper the existence and uniqueness of the solution for a generalized Boltzmann equation is proved and the positivity of this solution is discussed. Two series representations of the solution of the equation will be given.
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    On the integrability aspects of the one-dimensional classical continuum isotropic biquadratic Heisenberg spin chain (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1807-1816 
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    Notes: The integrability aspects of a classical one-dimensional continuum isotropic biquadratic Heisenberg spin chain in its continuum limit up to order [O(a4)] in the lattice parameter "a'' are studied. Through a differential geometric approach, the dynamical equation for the spin chain is expressed in the form of a higher-order generalized nonlinear Schrödinger equation (GNLSE). An integrable biquadratic chain that is a deformation of the lower-order continuum isotropic spin chain, is identified by carrying out a Painlevé singularity structure analysis on the GNLSE (also through gauge analysis) and its properties are discussed briefly. For the nonintegrable chain, the perturbed soliton solution is obtained through a multiple scale analysis.
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    Nondispersive solutions of the Dirac equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1822-1830 
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    Notes: Nondipersive solutions of the Dirac equation, that is, solutions depending on an arbitrary function F(u), where u is itself a solution of the characteristic equation (∇u)2−(c−1∂tu)2=0, are discussed.
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    A note on the construction of the C*-algebra of bosonic strings (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1837-1840 
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    Notes: This work continues investigations on the C*-algebra of bosonic strings started in Comm. Math. Phys. 136, 369 (1991). There a canonical section of a bundle was used implicitly in order to pass to an algebra of functions. In this article an algebra of sections is worked with directly. This clarifies the discussion on associativity of the algebra.
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    Bounds for the exact matrix elements for radiation processes in hydrogenic atoms (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1878-1886 
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    Notes: The exact matrix elements for transitions from the ground state to some excited state of a nonrelativistic hydrogenic atom, accompanied by the emission or absorption of a real or virtual photon, are here obtained in closed form. The matrix elements are simple rational functions of the photon energy if the excited state is bound, or have a simple transcendental factor if the excited state is unbound. It follows from the form of these elements that the contribution of each such process to the second-order radiative correction to the ground state energy level is always finite, without renormalization. It also follows that the sum of these contributions over all bound intermediate states is finite, while the sum over all unbound intermediate states diverges at most logarithmically without renormalization.
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    Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics−The quadratic profile (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1887-1914 
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    Notes: The application of phase space and path integral methods to both mathematical and computational direct and inverse wave propagation modeling at the level of the scalar one-way Helmholtz equation is briefly reviewed. The role of operator symbols is stressed and their properties briefly discussed. The construction of the operator symbol requires the exact or approximate solution of the (Helmholtz) Weyl composition equation in the Weyl pseudodifferential operator calculus. The exact symbols for several quadratic profiles are presented and briefly analyzed. The symbols exactly corresponding to a family of operator rational approximations are also presented for the quadratic case. These results are used to illustrate several points pertinent to wide-angle propagation modeling and the refractive index profile reconstruction problem in underwater acoustics.
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    Morse theory and gravitational microlensing (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1915-1931 
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    Notes: Morse theory is used to rigorously obtain counting formulas and lower bounds for the total number of images of a background point source, not on a caustic, undergoing lensing by a single-plane microlens system having compact bodies plus either subcritical or supercritical continuously distributed matter. An image-counting formula is also found for the case when external shear is added. In addition, it is proven that a microlens system consisting of k lens planes will generate N = 2M− + Πki=1(1 − gi) images of a background point source not on a caustic, where M− is the total number of critical points of odd index of the time-delay map and gi is the number of stars on the ith lens plane. Morse theoretic tools also yield that the smallest value N can have is Πi=1k(1+gi).
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    E(2)-symmetric two-mode sheared states (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1237-1246 
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    Notes: It is noted that the symmetry of two-mode squeezed states of light is governed by the group Sp(4) that is locally isomorphic to O(3,2). This group has subgroups that are locally isomorphic to the two-dimensional Euclidean group. Two-mode states having the E(2) symmetry are constructed. The translation-like transformations of this symmetry group shear the Wigner distribution function defined over the four-dimensional phase space consisting of two pairs of canonical variables. Sheared states are constructed in the Schrödinger picture of quantum mechanics and in the Fock space for photon numbers. It is shown that the Wigner phase-space picture is a convenient representation of quantum mechanics for calculating measurable quantities of the sheared states.
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    Erratum: Two-point functions and stress-energy tensors of p-forms in de Sitter and anti-de Sitter spaces [J. Math. Phys. 32, 2828 (1991)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1932-1932 
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    Canonical representations of sp(2n,R) (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1247-1251 
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    Notes: In this paper a rather unconventional real basis for the real symplectic algebra sp(2n,R) is studied. This basis is valid for representations carried by homogeneous polynomials of the 2n phase-space variables. The utility of this basis for practical computations is demonstrated by giving a simple derivation of the second- and fourth-order indices of irreducible representations of sp(2n,R).
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    C-Integrable nonlinear partial differential equations in N+1 dimensions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1257-1271 
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    Notes: Two techniques are introduced, which are suitable to manufacture C-integrable nonlinear PDEs (i.e., nonlinear PDEs solvable by an appropriate Change of variables) in N+1 dimensions. Several examples are exhibited.
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    Asymptotics of gravitational collapse of scalar waves (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1445-1457 
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    Notes: Through a combination of analytic and numerical techniques, the formation of a black hole by a self-gravitating, spherically symmetric, massless scalar field is investigated. The evolution algorithm incorporates a Penrose compactification so that the Bondi mass, the news function, and other radiation zone limits can be obtained numerically. The late time behavior recently established by Christodoulou is confirmed and new asymptotic relations for late time and for large amplitude limits are derived. For example, it is shown, that the Bondi mass MB and the scalar monopole moment Q satisfy the asymptotic relation MB∼ π||Q||/(square root of)2 at high amplitudes. It is found that the scalar monopole moment decays exponentially during black hole formation in contrast to the perturbation theory result for a power law decay rate in an Oppenheimer–Snyder background. It is demonstrated that the Newman–Penrose constant for the scalar field is globally well defined and has significant effects.
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    Einstein gravity coupled to a massless conformal scalar field in arbitrary space-time dimensions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1463-1471 
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    Notes: For space-times of arbitrary dimensionality two transformations are obtained that applied to any solution of the Einstein equations coupled to a minimally coupled scalar field construct a solution of the Einstein equations coupled to a conformal scalar field. The transformations are conformal for the metrics and algebraic for the reparametrization of the scalar fields. With these generating techniques static, spherically symmetric, asymptotically flat solutions of the Einstein-conformal scalar field equations in arbitrary space-time dimensions are obtained. Black hole solutions are systematically searched for and it is found that the only (nonvacuum) one exists in four space-time dimensions. This is the Bekenstein black hole for gravity coupled to a conformal scalar field.
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    Geometrization of a general collineation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1472-1479 
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    Notes: Geometrization of a general collineation means to express the collineation as necessary and sufficient conditions on the kinematic quantities (shear, vorticity, expansion) of the congruence of the vector field generating the collineation. It is shown that the generic form of a collineation is Lξgab = 2ψgab + Hab where Hab is a traceless symmetric tensor. A general theorem concerning the geometrization of the generic collineation is presented and its applications are discussed.
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    Quantized Arnold cat maps can be entropic K-systems (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1502-1510 
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    Notes: Automorphisms on the irrational rotation algebra with respect to their ergodic properties are studied. Especially it is shown that for a dense set of the rotation parameter θ cat maps are entropic K-systems.
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    A topological-field-theory approach to the non-Abelian Stokes theorem (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1511-1514 
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    Notes: A holomorphic path-integral representation for the parallel-transport and holonomy operator is derived. It is shown that a new form of the non-Abelian Stokes theorem follows from the Abelian Stokes theorem used for a topological field theory in an external gauge field.
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    Diffusive limits for particle transport in stochastic mixtures (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1480-1501 
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    Notes: Under the assumption of weak spatial and temporal gradients as well as weak absorption and sources, it is well known that the classic kinetic equation describing linear particle transport has a diffusion equation as an asymptotic limit. Considered here is such particle transport in a stochastic Markovian mixture of two immiscible fluids. It is shown that a variety of asymptotic diffusive limits exist under the scaling indicated above, depending upon the additional scaling introduced for the Markov transition lengths. These lengths are indicative of the mean chord lengths of the fluid packets in the stochastic mixture, and it is thus found that the details of the diffusive limits are strongly dependent upon the presumed sizes of the fluid packets. Asymptotically consistent initial and boundary conditions are also derived for each diffusion description obtained.
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    The propagator in the radial gauge (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1523-1528 
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    Notes: The solutions of the equation for the propagator in the radial gauge xμ Aμ(x) = 0 are studied. After finding a particular solution Γμρ(x,y), the most general solution G0μρ(x,y) of the homogeneous equation is written. It is shown that Γρμ(y,x) is not a solution; moreover, it is impossible to symmetrize Γμρ(x,y) by addition of a homogeneous solution. A "symmetrized'' generalization of the equation for the propagator is thus proposed. The photon propagator can also be calculated in this gauge using the field strength Fμρ(x), but it turns out to exist only in (4−ε) dimensions.
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    The fusion of R-matrices using the Birman–Wenzl–Murakami algebra (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1529-1537 
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    Notes: The action of the Birman–Wenzl–Murakami algebra is used as the centralizer of SOq(N) and Spq(N) to fuse Jimbo's trigonometric R-matrices and thus to construct new solutions of the Yang–Baxter equation.
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    Gauge equivalence theory of the noncompact Ishimori model and the Davey–Stewartson equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1515-1522 
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    Notes: The gauge equivalence between a noncompact version of the Ishimori spin model and the Davey–Stewartson equation is established. Explicit relationships connecting the corresponding two sets of fields involved in these systems are obtained via any pair of complex functions satisfying an equation of the Schrödinger type for a free particle. Using these formulas, two examples of classes of nontrivial exact singular solutions to the Davey–Stewartson equation are given. One of them is of the closed stringlike type, while the other is doubly periodic and is expressed in terms of Riemann theta functions. The role played by the symmetry group associated with the gauge equivalent equations under consideration is also clarified.
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    Realization of exceptional superalgebras in terms of fermion–boson creation–annihilation operators (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1538-1545 
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    Notes: Operators satisfying Clifford algebra (fermions) and Weyl algebra (bosons) are introduced. F(4) and G(3) are realized in terms of bilinears of fermions (the even part) and bilinears of one boson and one fermion (the odd part). D(2,1;α) is realized as bilinears (the even part) and trilinears (the odd part) of bosons.
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    On the geometry of spontaneous symmetry breaking (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1546-1549 
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    Notes: Given a principal bundle P→X with a structure group G and an associated Higgs bundle Σ with a standard fiber G/H, the case of a matter bundle E whose standard fiber admits action only of an exact symmetry subgroup H of G is examined. In the presence of a fixed Higgs field σ: X→Σ, matter fields are represented by sections of a matter bundle Eh associated with the corresponding reduced subbundle Ph of P. The totality of matter fields and Higgs fields is described by sections of the bundle E˜ which is the composite bundle EH→Σ→X where EH→Σ is the bundle associated with the principal H-bundle P→Σ. The bundle E˜ fails to be associated with a principal bundle. To construct a connection Γ: E˜→J1E˜ on E˜, the canonical jet bundle morphism J1EH×J1Σ→J1E˜ is used.
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    Erratum: "The Riemann–Hilbert problem for nonsymmetric systems'' [J. Math. Phys. 32, 3540 (1991)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1566-1566 
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    On the evaluation of the U(3) content of the matrix elements of one- and two-body operators (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1550-1565 
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    Notes: An expression for the U(3) content of the matrix elements of one- and two-body operators in Elliott's basis is obtained. Three alternative ways of evaluating this content with increasing performance in computing time are presented. All of them allow an exact representation of that content in terms of integers, avoiding rounding errors in the computer codes. The role of dual bases in dealing with nonorthogonal bases is also clarified.
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    Matrix elements and Wigner coefficients for Uq[gl(n)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1008-1022 
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    Notes: In this series of papers the fundamental Wigner coefficients and the matrix elements of the generators for the quantum group Uq[gl(n)] are derived. The Uq[gl(n)]:Uq[gl(n−1)] reduced Wigner coefficients and reduced matrix elements are determined algebraically as eigenvalues of certain Uq[gl(n−1)] invariants in the quantum group Uq[gl(n)]. The matrix elements of the elementary quantum group generators, in the Gel'fand–Tsetlin basis, are derived below, while all fundamental Wigner coefficients are derived in the second paper of the series.
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    Reduced Wigner coefficients for Uq[gl(n)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1023-1031 
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    Notes: This is the second paper in a series concerned with the Racah–Wigner calculus for the quantum group Uq[gl(n)]. In this approach all reduced Wigner coefficients are determined algebraically by the eigenvalues of certain generalized Casimir invariants. Here the method is applied to evaluate all fundamental Wigner coefficients and reduced Wigner coefficients for Uq[gl(n)].
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    The initial value problem for a class of general relativistic fluid bodies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1047-1053 
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    Notes: A body or collection of bodies made of perfect fluid can be described in general relativity by a solution of the Einstein–Euler system where the mass density has spatially compact support. It is shown that for certain equations of state there exists a wide class of solutions of this type corresponding to appropriate initial data given on a spacelike hypersurface. This class is not constrained by any symmetry requirements. The key element of the proof is to write the equations as a symmetric hyperbolic system which is regular both for nonvanishing density and in vacuum.
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    A superversion of quasifree second quantization. I. Charged particles (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1032-1046 
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    Notes: A formalism comprising and extending quasifree second quantization of charged bosons and fermions is presented. The second quantization of one-particle observables leads to current superalgebras, and a super-Schwinger term shows up. Anticommuting parameters are introduced in order to construct super-Bogoliubov transformations mixing bosons and fermions. As an application, representations of Lie superalgebras are given which are semidirect products of extensions of affine Kac–Moody algebras and the Virasoro algebra, and of the super-Virasoro algebra.
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    Head-on collision of gravitational plane waves with noncollinear polarization: A new class of analytic models (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1054-1064 
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    Notes: A new four-parameter class of exact solutions of Einstein's field equations is obtained, using the inverse scattering method of Belinsky and Zakharov. Its members represent the head-on collision of a variably polarized gravitational plane wave with one having constant polarization and, in general, different profile, or with an infinitely thin shell of null dust. In some of these models no curvature singularity develops along the future boundary of the region of interaction. In certain cases the singularity avoidance is the direct result of the noncollinear polarization of the waves involved in the collision.
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    Gravitational interaction of plane gravitational waves and matter shells (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1065-1072 
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    Notes: The Weyl, Ricci scalars and the Bianchi identities are explicitly given in terms of distributions. Using the obtained Bianchi identities, the gravitational interaction of colliding shock or impulsive gravitational plane waves or matter shells is studied. It is found that, when two impulsive shells of null dust collide, they necessarily produce a tail. The tail could be a "Coulomb-like'' gravitational field, or a matter current, or a mixture of both.
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    Exact partition functions of interacting lattice fermions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1082-1089 
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    Notes: Exact expressions are obtained for Grassmann integrals of exponentials corresponding to the partition functions of systems of lattice fermions with nearest-neighbor interactions. It is achieved by relating to the dimer problem and use of its combinatorial techniques.
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    Minimal coupling of electromagnetic fields in Riemann–Cartan space-times for perfect fluids with spin density (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1073-1081 
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    Notes: The electromagnetic field is minimally coupled to gravity in a Riemann–Cartan space-time containing a charged magnetized spinning fluid. It is required that the overall Lagrangian of the gravitational field, spinning matter, and the electromagnetic field be invariant under a gauge transformation of the vector potential. The theory preserves both charge conservation and particle number conservation. The electromagnetic field, via the vector potential, now interacts directly with the spin energy momentum. The spin transport equation, in addition to the usual Fermi–Walker transport term, contains a contribution due to the torque of the electromagnetic field acting on a magnetic dipole. In the absence of electromagnetism, the field equations reduce to those of the usual self-consistent Lagrangian formalism for a perfect fluid with spin density.
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    Concomitants theory and renormalization in even dimensions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1097-1102 
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    Notes: The complete set of concomitants is given of the metric, a scalar function, and their derivatives in six dimensions without imposing conditions on the order of the derivatives and their properties are studied under conformal transformations. These results are useful in several physical problems, like finding 〈cursive-phi2〉ren and 〈Tμν〉ren in any geometry.
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    Z3 -graded algebras and the cubic root of the supersymmetry translations (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 403-411 
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    Notes: A generalization of supersymmetry is proposed based on Z3 -graded algebras. Introducing the objects whose ternary commutation relations contain the cubic roots of unity, e2πi/3, e4πi/3 and 1, the operators whose trilinear combinations yield the supersymmetric translation generators can be constructed. Cubic matrices forming a ternary algebra are the generalization of Pauli's matrices. The general properties of Z3 -grading, some other representations of such algebras, and their possible pertinence with regard to the quark model are briefly discussed.
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    On the group aspects of Riemann–Hilbert transformations (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 56-63 
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    Notes: The more general algebraic structures of two-dimensional integrable systems are derived in a model independent manner by using the infinitesimal Riemann–Hilbert transformation. It is found that the resulting algebra decomposes into many families and, for each family, there is a Lie multialgebra structure. Examples of the chiral sigma models, four-dimensional self-dual Yang–Mills field, sine–Gordon, and Liouville equations and the BZ gravity are given with two special Lie products equipped therein.
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    The general solution of the three-dimensional acoustic equation and of Maxwell's equations in the infinite domain in terms of the asymptotic solution in the wave zone (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 86-101 
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    Notes: The general solution of the three-dimensional scalar wave equation (or acoustic equation) and of Maxwell's equations in the infinite spatial domain is given in terms of the asymptotic forms for large times in the future and in the past, or, equivalently, in terms of the fields in the wave zone. One is therby able to obtain the exact solutions from arbitrary solutions in the wave zone. It is shown that the exact fields computed from an arbitrary wave zone solution always satisfy an initial value problem, and that, therefore, they are always physical. In contrast to earlier derivations of related results which required the use of Radon transforms and the introduction of somewhat sophisticated geometrical concepts, the derivations are simple and use only elementary properties of the Fourier transform.
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    Arithmetic features of 2-D strings (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1148-1152 
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    Notes: The on-shell tree amplitudes of 2-D P-adic strings are constructed. Along with the recently obtained on-shell tree amplitudes of the ordinary (archimedean) 2-D string, they lead to adelic product formulas for all N-point amplitudes. This is in marked difference from 26-D critical strings, where such adelic formulas only obtain for four-point amplitudes. Certain much-discussed operator redefinitions are considered at the P-adic level where they change radically, the P-adic gamma function having only one rather than infinitely many real poles. Also considered are q-strings in 2-D.
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    URL: http://dx.doi.org/10.1063/1.529727
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    Eigenfunctions and heat kernels of super Maass Laplacians on the super Poincaré upper half-plane (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1158-1177 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Heat kernels of "super Maass Laplacians'' are explicitly constructed on super Poincaré upper half-plane by a serious treatment of a complete set of eigenfunctions. By component decomposition an explicit treatment can be done for arbitrary weight and a knowledge of classical Maass Laplacians becomes helpful. The result coincides with that of Aoki [Commun. Math. Phys. 117, 405 (1988)] which was obtained by solving differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529974
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    Topological aspects of Liouville field theory and conformal anomaly (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1178-1184 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that conformal anomaly is connected with the topological properties of the Liouville field theory which arises out of the quantum geometry necessary for the quantization procedure. As in the particle picture, the quantization of a Fermi field can be achieved through the introduction of an anisotropic feature in the internal space so that it gives rise to two internal helicities corresponding to particle and antiparticle, in case of a string, also, this specific quantum geometry gives rise to two vortex lines at the endpoints of an open string which is manifested in the Liouville field theory. This helps one to represent a Polyakov string with a nonlinear σ model with the Wess–Zumino term, and the topological aspects of this Wess–Zumino term is found to be associated with those of a Liouville field. When in the Lagrangian formulation this specific quantum geometry is taken into account, it is found that anomaly vanishes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529729
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    Soliton solutions to coupled higher-order nonlinear Schrödinger equations (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1208-1215 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A set of coupled higher-order nonlinear Schrödinger equations, which describe electromagnetic pulse propagation in coupled optical waveguides, is formulated in terms of an eigenvalue problem. Using that result, the inverse scattering problem is solved and explicit soliton solutions are found. Additionally, linear coupling terms are studied systematically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529732
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    Linear undulator brightness: Exact analytical treatment (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1200-1207 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper it is shown that the calculation of linearly polarized undulator brightness can be worked out exactly using elliptic functions and multivariable generalized Bessel functions. The obtained results are shown to be valid both in nonrelativistic and ultrarelativistic regimes. The physical relevance of the obtained results are discussed and the "low-energy'' corrections to the resonance condition are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529731
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    Movable singularities in Sigma and Skyrme models (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1185-1199 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The singularity structure of the solutions of the equations of motion for the Sigma and Skyrme model Lagrangians with the hedgehog ansatz is investigated. In both cases the solutions present superposed a polelike term and a logarithmic branch point. The set of solitonic configurations of the Skyrme model is characterized by the sequence of locations of their singularities on the negative real axis of the dimensionless variable z = (eFπr)2, with an accumulation point at z=0. The first few terms of the Laurent series representing the Skyrme soliton profile are shown to reproduce well the exact values in an interval about the origin. Padé approximants to the residual power series obtained after subtraction of the dominant pole term are modified in order to satisfy the constraints imposed by the asymptotic power series expansion, and approximate representations are built for the Skyrme soliton configuration, which are shown to combine simplicity with accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529730
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    An application of first integrals method in magnetic diffusion problem (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1216-1220 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper a rigorous approach to the magnetic diffusion problem is presented under the assumption that the random fluid velocity field is independent of x and completely determined by a prescribed probability measure on the space of symmetric velocity field u(t)=u(−t). By adopting the first integrals method developed by Visik and Fursikov [Mat. Sb. 92, 347 (1973)], the space characteristic functional associated with the random induction equation has been expressed by a functional power series. The explicit formula for this functional has been obtained, without deriving and solving a suitable functional equation for the [u,B] field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529984
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    Novel symmetry of non-Einsteinian gravity in two dimensions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3892-3900 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The integrability of R2-gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space. It may be interpreted as a quadratically deformed iso(2,1)-algebra with the deformation consisting of the Casimir operators of the undeformed algebra. The locally conserved quantity encountered in the explicit solution is identified as an element of the center of this algebra. Specific contractions of the algebra are related to specific limits of the explicit solutions of this model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529836
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    A simple method for group analysis and its application to a model of detonation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3931-3937 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple procedure is suggested to obtain extensions of the principal Lie algebra, for invariance transformations of a given family of equations, by using an equivalence algebra. An application to a qualitative model of detonation is performed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529841
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    Exact wave functions of an electron on a quasiperiodic lattice: Definition of an infinite-dimensional Riemann theta function (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3938-3947 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A scheme for obtaining the exact wave functions of an electron on a quasiperiodic lattice is presented. It is shown that the trace map plays a very important role for construction of the infinite-dimensional Riemann theta function in terms of which the wave functions can be represented.
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    URL: http://dx.doi.org/10.1063/1.529842
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    A contribution to nonstandard superanalysis (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3263-3273 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The nonstandard (infinitesimal) analysis developed by Robinson is applied to certain foundational aspects of superanalysis. The construction of nonstandard hull due to Luxemburg is used to study "limit phenomena'' arising in a Grassmann algebra Λ(q) as the number of generators q tends to infinity. An outcome of such an approach is that under transition t→∞ a superspace of purely odd dimension (0,q) transforms into a superspace of dimension (∞,∞) and not (0,∞) as one would expect. It is suggested that this construction may have something to do with the problem of adequate mathematical description of collective bosonic effects arising within infinite fermionic dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529930
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    Stability of Hamiltonian systems at high energy (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3367-3373 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Let H=T(P)+U(P,cursive-phi) be the Hamiltonian for a classical mechanical system of l degrees of freedom, where T is an integrable Hamiltonian generating quasiperiodic motion in the first l−1 degrees of freedom which has the form
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    URL: http://dx.doi.org/10.1063/1.529937
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    On pararelativistic quantum oscillators (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3387-3392 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Different choices of matrices characterizing p=2 parafermions are analyzed in connection with the description of relativistic spin-one particles through the Kemmer formulation. The free and interacting cases are considered and the relations between parasupersymmetry and Kemmer theory are enhanced as it is also the case between supersymmetry and Dirac theory. In that way the oscillatorlike context leads to the characterization of pararelativistic oscillators.
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    URL: http://dx.doi.org/10.1063/1.529886
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