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1

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General method for reducing the two-body Dirac equation (1992)

Galea˜o, A. P. ; Ferreira, P. Leal

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 2618-2625

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

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)

Ferreira, Erasmo ; Neto, Jorge Ananias

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 2626-2632

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.529581

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3

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Weyl manifolds and connections (1992)

Hall, G. S.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 2633-2638

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

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)

Malvagi, F. ; Sammartino, M. ; Pomraning, G. C.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 2639-2647

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

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)

Klimyk, A. U. ; Pakuliak, S. Z.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 1937-1947

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

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)

Healy, Liam M. ; Dragt, Alex J. ; Gjaja, Ivan M.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 1948-1963

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

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)

Zhang, R. B.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 1970-1979

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

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)

Sullivan, J. J. ; Siddall, T. H.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 1964-1969

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

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)

Ališauskas, S.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 1980-1982

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

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)

Ališauskas, Sigitas

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 1983-2004

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.529622

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