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  • Articles  (349,175)
  • Elsevier  (338,784)
  • American Institute of Physics (AIP)  (10,391)
  • Mathematics  (349,175)
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  • 1
    Electronic Resource
    Electronic Resource
    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
    Electronic Resource
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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
    Electronic Resource
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529669
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  • 6
    Electronic Resource
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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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    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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  • 25
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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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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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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    Topics: Mathematics , Physics
    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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    Topics: Mathematics , Physics
    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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    Topics: Mathematics , Physics
    Notes: The massive p-form two-point functions in maximally symmetric spaces of arbitrary dimension n are obtained.
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    Spherically symmetric scalar fields (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2468-2472 
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    Notes: The Einstein equations coupled with a spherically symmetric time-dependant scalar field are solved. The problem of two distinct cases is reduced and the first of them is successfully solved completely, the resulting solutions being cosmological models. For the second one which is static, only a partial solution is found.
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    First integrals for the equations of motion for test particles with internal structure (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2473-2477 
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    Notes: In the framework of a general Lagrangian approach to the equations of motion for test particles with internal structure symmetry conditions and the corresponding conserved quantities are derived. As simple examples, first integrals of the equations of geodesic deviation, the Mathisson–Papapetrou and the Wong equations are rediscovered.
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    Separation of variables for the Dirac equation in an extended class of Lorentzian metrics with local rotational symmetry (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2497-2502 
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    Notes: The question of the separability of the Dirac equation in metrics with local rotational symmetry is reexamined by adapting the analysis of Kamran and McLenaghan [J. Math. Phys. 25, 1019 (1984)] for the metrics admitting a two-dimensional Abelian local isometry group acting orthogonally transitively. This generalized treatment, which involves the choice of a suitable system of local coordinates and spinor frame, allows one to establish the separability of the Dirac equation within the class of metrics for which the previous analysis of Iyer and Vishveshwara [J. Math. Phys. 26, 1034 (1985)] had left the question of separability open.
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    Extended gauge theories (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2503-2512 
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    Notes: A scheme inspired in Lie algebra extensions is introduced that enlarges gauge models to allow some coupling between space-time and gauge space. Everything may be written in terms of a generalized covariant derivative including usual differential plus purely algebraic terms. A noncovariant vacuum appears, introducing a natural symmetry breaking, but currents satisfy conservation laws alike those found in gauge theories.
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    On the isovectors of the principal chiral model (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2540-2542 
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    Notes: In this paper the principal chiral model with isovector techniques is dealt with [B. K. Harrison and F. B. Estabrook, J. Math. Phys. 12, 653 (1971); C. J. Papachristou and B. K. Harrison, J. Math. Phys. 28, 1261 (1987)]. Due to the "on shell'' property of the symmetry related to integrability [M. L. Ge and Y. S. Wu, Phys. Lett. B 108, 411 (1982), L. L. Chau, M. L. Ge, and Y. S. Wu, Phys. Rev. D 25, 1086 (1982); B. Y. Hou, M. L. Ge, and Y. S. Wu, Phys. Rev. D 24, 2238 (1981)], the linear system is derived from the internal part of the isogroup after the determining equation is localized. When the geometric part of the derived isovectors is analyzed, a set of operators acting on space-time are found, which make up an infinite-dimensional invariant algebra of the principal chiral model.
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    Anomaly meltdown (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1981-1983 
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    Notes: It is shown that at nonzero temperature it is possible that anomalies in representations of symmetry groups and gauge groups, present at zero temperature, disappear. Several examples are given. Thus the idea that anomalies in baryon currents might have caused the baryon imbalance in the early hot universe needs reconsideration.
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    Space-time geometry of relativistic particles in four-dimensional phase space (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1998-2006 
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    Notes: The Wigner phase-space picture of Dirac's two-oscillator representation of O(3,2) is given. This constitutes a real representation of Sp(4) which allows us to study the symmetry of the O(3,2) de Sitter group using canonical transformations in four-dimensional phase space. It is also possible to study subgroups of O(3,1) in this phase space. The phase-space picture is given for the two-oscillator model of van Dam, Ng, and Biedenharn [Phys. Lett. B 158, 227 (1985)] for the little groups for massive and massless particles. In this formalism, Lorentz transformations can be described in terms of canonical transformations in phase space. It is particularly convenient for studying infinite-momentum/zero-mass limit of the O(3)-like little group for a massive particle. It is shown that the trivial representation of the E(2)-like little group for a massless particle emerges from this limiting process. The origin of gauge degree of freedom is discussed.
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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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    Heat equation asymptotics of "nonminimal'' operators on differential forms (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2089-2091 
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    Notes: Let D=αdδ+βδd−E be a natural operator on differential forms. For example, (Dv)j=−(large-closed-square)k∇kvj−C1(large-closed-square)j∇kvk +C2Rjkvk has this form. It will be shown that when the lower-order term E is absent, the integrated heat kernel coefficients an(D) can be simply expressed in terms of the (familiar) coefficients an(Δj) for the Laplacian operators on forms. The first two coefficients when a zeroth-order term is present are evaluated.
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    Non-Riemannian model of the space-time responsible for quantum effects (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2092-2098 
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    Notes: A class of homogeneous isotropic space-time models including pseudo-Euclidean space as a special case is considered. Such a model is chosen, where the particle motion is described in the most adequate way. It means that the world tubes of all free particles (both classical and quantal) are characteristic geometrical structures of the space-time. The world function σ of this model has the form σ=σE+σ0, σE〉σ0 where σE is the world function of the pseudo-Euclidean space, σ0 is a constant responsible for quantum effects. It is proportional to Planck's constant (h-dash-bar).
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    The Feynman integrand as a Hida distribution (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2123-2127 
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    Notes: It is shown that Feynman integrals are weighted averages over Brownian paths, with suitable Hida distributions as (complex) weights. For simple cases, the construction of these distributions is be performed explicitly, for a much larger class of interactions, their existence is shown.
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    Continuous quantum jumps and infinite-dimensional stochastic equations (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2152-2157 
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    Notes: From a mathematical point of view, a class of infinite-dimensional stochastic differential equations describing continuous spontaneous localization in quantum dynamics will be studied. Existence and uniqueness of weak and strong solutions of respective equations are proven via Cameron–Martin–Girsanov transformation. The case of Gaussian initial states is explicitly solved.
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    Chern–Simons terms in metric-affine space-time: Bianchi identities as Euler–Lagrange equations (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2169-2180 
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    Notes: The metric-affine gauge theory of gravity encompasses a space-time with the following geometrical fields: coframe cursive-thetaα, metric g, and an independent linear connection Γαβ. Within this geometrical framework, all four-forms B=dC are constructed which qualify as boundary terms for a gauge Lagrangian, that is, they are GL(4,R)-scalars as well as exact forms derived from Chern–Simons type three-forms C. The result of our search is summarized in Eq. (4.20). The translational piece dCTT is new. The boundary terms effectively serve as Lagrangians for the Bianchi identities of nonmetricity, torsion, and curvature. In the canonical formalism, the normal parts of the Chern–Simons three-forms represent generating functions that are capable of generating new Ashtekar type variables. Eventually, the Bach–Lanczos identity is generalized to the metric-affine space-time.
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    Analytic solution to the Thomas–Fermi and Thomas–Fermi–Dirac–Weizsäcker equations (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2250-2253 
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    Notes: A novel method for solving the Thomas–Fermi and Thomas–Fermi–Dirac–Weizsäcker equation at zero temperature is explored. The fitting formulas for the effective potential and the electron density derived from this theory can serve as appropriate initial input to various computer codes designed to analyze the statistical model of atoms and molecules. One of the important parametrizations for the Thomas–Fermi–Dirac–Weizsäcker equation is that the density at the center of the atom is finite and proportional to the cube of the atomic number with a constant of proportionality nearly equal to 6.87.
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    On a double Riemann–Hilbert approach to stimulated Raman scattering (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2254-2257 
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    Notes: The inverse problem for stimulated Raman Scattering (SRS) with the help of an extension of usual Riemann-Hilbert methodology is considered. The same problem was previously considered by Kaup and Steudel from the viewpoint of scattering formalism. Actually, the Riemann–Hilbert transform has been used for both the x and t part of the Lax pair separately and it has been called double Riemann–Hilbert approach. When compared with the treatment of Kaup and Steudel, the simplicity of our approach becomes quite evident, although it is not still possible to solve an initial-boundary value problem in the present scheme as done by Kaup and Steudel.
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    Spherically symmetric density perturbation in relativistic cosmology (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2279-2282 
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    Notes: Einstein's field equations for spherically symmetric perfect fluids are reduced to two equations plus three definitions, and from these the spherical density perturbation equation is derived. It is found that this perturbation equation can be separated into two equations by the method of separation of variables and can be solved explicitly in some special cases. An interesting result is that for matter-dominated era the perturbation equation is found to be of the Bonnor form of Newtonian theory. Another interesting result is that for zero-curvature universe and radiation-dominated era the density perturbation has two growing modes: one is something like a power of the proper time, and the other is of the exponential law of the conformal time, each corresponds to a different limit of approximation.
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    Effective Hamiltonian within the microscopic unitary nuclear model. I: Coherent-state restriction technique for microscopic Hamiltonian (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1683-1695 
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    Notes: A technique of projecting the microscopic nuclear Hamiltonian on the SU(3) group enveloping algebra is developed. The proposed approach is based on the effective Hamiltonian restoring from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation.
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    On the application of maximum entropy to the moments problem (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1717-1719 
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    Notes: The use of the maximum entropy condition to obtain a solution to the moments problem, in which one seeks to reconstruct a function from the values of a finite set of its moments, is of interest in a variety of physical applications. Unfortunately, the standard analysis which is available, and on which these applications are based, takes as its starting point precise values of the moments whereas the physical applications involve imprecise data. In this paper it will be shown how to solve the moments problem, using the maximum entropy condition, starting from imprecise data values with errors specified by a χ2 -function.
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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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    Erratum: Covariant quantization of gauge theories in the framework of extended BRST symmetry [J. Math. Phys. 31, 1487 (1990)] (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1970-1970 
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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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    Properties of second-order ordinary differential equations invariant under time translation and self-similar transformation (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1480-1490 
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    Notes: The general form of a second-order ordinary differential equation invariant under time translation and self-similarity is obtained together with its solution in parametric form. Next two representatives of two different families of such equations are studied. In terms of rescaled phase space variables, the first example has a simple physical interpretation and its limit cycle properties and period are easily derived. Similar results are found for the second example, but the physical interpretation is less obvious. The invariant equations are used as a basis to study the asymptotic behavior of related noninvariant equations thereby underlining the critical value nature of the parameters for which a self-similar solution (SSS) exists.
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    Symmetries and degeneracies of a charged oscillator in the field of a magnetic monopole (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1516-1521 
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    Notes: The constants of motion responsible for the level degeneracy of a charged, spin 0 particle subjected to harmonic and centrifugal forces and to the field of a magnetic monopole are obtained. Operators closing onto the SU(2)⊕SU(2) algebra are constructed in terms of these conserved quantities. The space of states decomposes into SU(2)⊕SU(2) irreducible modules whose dimensions coincide with the degree of degeneracy of the various energy levels.
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    Similarity reduction of the one-Killing-vector vacuum equations in general relativity (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1552-1555 
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    Notes: The one-Killing-vector vacuum equations are a set of partial differential equations in three independent variables. To make them tractable, one usually assumes the existence of a second commuting Killing vector field. In this paper, the full set of Lie-point symmetries of the equations and the related (other) possible reductions to differential equations in two independent variables are discussed.
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    The weak coupling limit for Fermions (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1567-1581 
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    Notes: It will be shown that, in the weak coupling limit, the matrix elements in the collective number vectors of the evolution in the interacting picture of a quantum system coupled to a quasifree Fermion bath with a laser type interaction, converge to the matrix elements in some number vectors, of a unitary quantum stochastic process satisfying a quantum stochastic differential equation driven by a Fermion Brownian motion with covariance uniquely determined by the initial Fermion bath.
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    Multivectorial generalization of the Cartan map (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1591-1598 
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    Notes: A multivectorial generalization of the spinors to vectors Cartan map is constructed, with space-time as a base space, constructed from spinors (Dirac spinors and spinors pairs being particular cases) onto a multivector space with two internal symmetries: one of them is the fundamental space-time Clifford group C(1,3) and the other an "isotopic space'' (in multivectorial representation) related with the more common gauge groups. The algebraic properties of this map and of the operators representing observables are studied. The inversion map is also presented. The quaternion projection of the map is shown as are its properties and its mathematical and physical meaning. The procedure presented here is compared with other spinor-vector maps used in the literature.
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    High-energy, large-momentum-transfer processes: The N-rung ladder diagram of cursive-phi3 theory (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1619-1637 
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    Notes: The asymptotic form of the amplitude for the N-rung ladder diagram in cursive-phi3 theory is calculated in the limit s(very-much-greater-than)||t||(very-much-greater-than)m2. The result is proportional to s−1||t||−N+1 times a homogeneous polynomial of degree 2N−2 in ln s and ln||t||. It is not an analytic function of s and t, although the first N+1 derivatives are continuous in the physical region. Points of nonanalyticity occur when ln||t||=γ ln s for γ= (1)/(2) , (1)/(3) ,..., 1/(N−2). The notion of reduced Symanzik functions is introduced. With the aid of these reduced Symanzik functions, a generating function is derived for the leading logarithms of all ladder diagrams.
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    On the characters of solvable finite groups (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1150-1154 
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    Notes: A method to calculate the characters of a finite group in terms of the characters of a normal subgroup is proposed with the only condition that the factor group may be a cyclic group of prime order. The method can also be used recursively to calculate the characters of any solvable finite group.
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    The three-dimensional Euclidean quantum group E(3)q and its R-matrix (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1159-1165 
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    Notes: A contraction procedure starting from SO(4)q is used to determine the quantum analog E(3)q of the three-dimensional Euclidean group and the structure of its representations. A detailed analysis of the contraction of the R-matrix is then performed and its explicit expression has been found. The classical limit of R is shown to produce an integrable dynamical system. By means of the R-matrix the pseudogroup of the noncommutative representative functions is considered. It will finally be shown that a further contraction made on E(3)q produces the two-dimensional Galilei quantum group and this, in turn, can be used to give a new realization of E(3)q and E(2,1)q.
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    The Stratonovich–Weyl correspondence for one-dimensional kinematical groups (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1182-1192 
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    Notes: The Stratonovich–Weyl correspondence is a restatement of the Moyal quantization where the phase space is a manifold and where a group of transformations acts on it transitively. The first and most important step is to define a mapping from the manifold into the set of self-adjoint operators on a Hilbert space, under suitable conditions. This mapping is called a Stratonovich–Weyl kernel. The construction of this mapping is discussed on coadjoint orbits of the one-dimensional Galilei, Poincaré, and Newton–Hooke groups as well as the two-dimensional Euclidean group.
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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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    The Riemann–Hilbert problem approach to a representation of the Virasoro group II (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1328-1333 
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    Notes: The development of a Riemann–Hilbert (RH) problem approach to the representation of the Virasoro group introduced in our earlier paper [W. Li and B. Y. Hou, J. Math. Phys. 30, 1198 (1989)] is continued. The Rouche theorem is employed to prove that there exists a set of scalar functions in the complex τ plane, in terms of which the structure of the Virasoro group can be decided. The general form of the RH problem will also be presented and the uniqueness of its solution will be proven. For future use, a standard form of a matrix Fredholm equation equivalent to our RH problem will be deduced. This may help to establish in a future paper the existence of a solution of the RH problem.
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    Unimodular theory of gravity and the cosmological constant (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1337-1340 
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    Notes: The unimodular theory of gravity with a constrained determinant gμν is equivalent to general relativity with an arbitrary cosmological constant Λ. Within this framework Λ appears as an integration constant unrelated to any parameters in the Lagrangian. In a quantum theory the state vector of the universe is thus expected to be a superposition of states with different values of Λ. Following Hawking's argument one concludes that the fully renormalized Λ=0 completely dominates other contributions to the integral over Λ in the vacuum functional. In this scenario of the unimodular theory of gravity the cosmological constant problem is solved. Furthermore, this formulation naturally provides an external (cosmic) time for time ordering of measurements so that the quantum version of the unimodular theory can have a normal "Schrödinger'' form of time development, giving a simpler interpretation to the equation of the universe.
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    Reasons for a physical field to obey linear partial differential equations (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1354-1359 
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    Notes: Fields showing a deterministic evolution, which is linear and local, can be described by a linear system of partial differential equations.
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    The action principle revisited (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1376-1382 
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    Notes: The form of Schwinger's action principle within the BPHZ method is investigated and some loopholes in the usual proofs are closed.
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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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    URL: http://dx.doi.org/10.1063/1.529666
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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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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529667
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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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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529701
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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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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529668
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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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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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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    URL: http://dx.doi.org/10.1063/1.529702
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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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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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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    URL: http://dx.doi.org/10.1063/1.529973
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    Covariant Lax operators and Kac–Moody algebras (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 869-874 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It will be shown that covariantizing the Lax operators with a "time'' independent non-Abelian gauge connection leaves the dynamical equations invariant. However, the symmetries associated with the Schrödinger equation in such a case is enlarged. This is used to give a simple derivation of various Kac–Moody algebras associated with such Lax operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529345
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    Methods of holonomy theory for Ricci-flat Riemannian manifolds (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 888-896 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Compact, Ricci-flat Riemannian manifolds often arise in physical applications, either as a technical device or as models of "internal'' space. The idea of extending the holonomy group of such a manifold to a larger gauge group ("embedding the connection in the gauge group'') plays a fundamental role in the "manifold compactification'' approach to superstring phenomenology, and the work of Gepner suggests that this idea may have equally fundamental analogs in other approaches. The holonomy theory of simply connected Ricci-flat manifolds has recently been the subject of much mathematical work, but physicists are mainly interested in the case of multiply connected manifolds. The purpose of this paper is to present some techniques for understanding the holonomy theory of compact, multiply connected Ricci-flat manifolds. These lead to a general classification theorem.
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    URL: http://dx.doi.org/10.1063/1.529347
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    Nonlinear reactor multigroup neutron transport system: Existence and stability problems (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 905-915 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This article considers a system of nonlinear transport equations describing multigroup neutron fission and scattering, coupled with temperature feedback. Various possibilities of temperature feedbacks are studied. Existence, together with upper and lower bounds of solutions are considered. Sufficient conditions for stability and instability are given for various feedbacks.
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    URL: http://dx.doi.org/10.1063/1.529349
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    p-adic quantum mechanics with p-adic valued functions (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 932-937 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An extension of the formalism of quantum mechanics to the case where the canonical variables and functions are valued in a field of p-adic numbers is considered. A new p-adic integral calculus is used for the realization of the Gauss representation in p-adic quantum mechanics.
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    URL: http://dx.doi.org/10.1063/1.529353
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    Transformation properties of the Schrödinger equation with the momentum-dependent potential (x⋅∇)2ord (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 967-970 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using suitable coordinate transformations enables us to convert the Schrödinger equation with the momentum-dependent potential (x⋅∇)2ord into a pair of coupled s-wave Pöschl–Teller systems with zero energy. An equivalent zero-energy system with a related singular potential has also been derived, this time by using an appropriate wavefunction transformation.
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    URL: http://dx.doi.org/10.1063/1.529357
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    Orthogonalization coefficients for the Elliott–Draayer states of the two parametric irreps of SU(n)&supuline;SO(n) (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 569-575 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Explicit algebraic-polynomial expressions for the direct and inverse orthogonalization coefficients of the projected (Elliott–Draayer) basis states of SU(n)&supuline;SO(n) are constructed in the case of two parametric irreducible representation (irreps). They cover the general SU(3)&supuline;SO(3) case as well as the two parametric covariant irreps of SU(4) restricted to the SU(2)×SU(2) subgroup of spin and isospin. The obtained orthonormal bases are equivalent to those constructed by means of the ordered Gram–Schmidt process. The orthogonalization coefficients are expressed, up to explicitly given elementary factors, in terms of the numerator and denominator polynomials related with those that appeared in the orthogonalization coefficients of the paracanonical coupling coefficients (isofactors) of SU(3) and with Aλ functions of Louck, Biedenharn, and Lohe.
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    URL: http://dx.doi.org/10.1063/1.529396
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    Clifford algebra: Notes on the spinor metric and Lorentz, Poincaré, and conformal groups (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 576-583 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A particular normalization for the set of basis elements {Γi} of the complex Clifford algebras C(p,q) is motivated and defined by demanding that the physical bispinor densities ρi=Ψ¯ΓiΨ be real. This condition, referred to here as Dirac normalization, also necessitates the introduction of the spinor metric γ, and the solution of the metric conditions is given for arbitrary (p,q); when N=p+q is even the metric is unique, and when N is odd there are two distinct metrics. Then the Dirac normalization preserving automorphism group of the basis is explored. This is also the group of transformations leaving the spinor metric invariant. In particular, the physically important cases of the Lorentz, Poincaré, and conformal groups are sought as subgroups of the automorphism group. As expected, it is found that the Lorentz group is always contained in the automorphism group. However, it is found that the Poincaré and conformal groups are contained only in the cases where N is even and q is odd. Furthermore, when N is odd these groups may be found in the full isomorphism group, but only for one of the two possible spinor metrics. Possible physical implications of these results are discussed.
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    URL: http://dx.doi.org/10.1063/1.529397
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