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  • 1
    Electronic Resource
    Electronic Resource
    Minimization of Landau potentials invariant under O(3).II (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1300-1303 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In a previous paper, the absolute minima for Landau potentials were computed for the irreducible representations of SO(3) or O(3) of spin up to four. Here, this analysis is extended to the case of spin five and six. Some novel properties of the extrema are pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528767
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  • 2
    Electronic Resource
    Electronic Resource
    Real representations of Clifford algebras (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1579-1581 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Simple proof of classification theorem of all real irreducible representations of Clifford algebras is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529682
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  • 3
    Electronic Resource
    Electronic Resource
    Dyon-Skyrmion lumps (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1136-1152 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We make a numerical study of the classical solutions of the combined system consisting of the Georgi–Glashow model and the SO(3) gauged Skyrme model. Both monopole-Skyrmion and dyon-Skyrmion solutions are found. A new bifurcation is shown to occur in the gauged Skyrmion solution sector. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532793
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  • 4
    Electronic Resource
    Electronic Resource
    Linear operators with invariant polynomial space and graded algebra (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 989-999 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The irreducible, finite-dimensional representations of the graded algebras osp(j,2) (j=1,2,3) are expressed in terms of differential operators. Some quantum deformations of these algebras are shown to admit similar kinds of representations. These are formulated in terms of finite difference operators. The results are discussed in the framework of the quasi-exactly solvable equations. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531806
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  • 5
    Electronic Resource
    Electronic Resource
    Quasi exactly solvable extensions of the Lamé equation (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 5283-5291 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quasi exactly solvable equations are spectral equations which possess a finite number of algebraic eigenvectors. For a few of these equations, such as the Lamé equation, the number of algebraic solutions is larger than predicted by the general theory. A class of quasi exactly solvable equations in one variable is considered and the conditions under which a rich algebraization occurs is discussed. Families of equations, which by themselves are not quasi exactly solvable, but can be transformed into systems of coupled quasi exactly solvable equations, are discussed. These results suggest a scheme for the classification of quasi exactly solvable systems in one variable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530304
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  • 6
    Electronic Resource
    Electronic Resource
    Instantons in four-dimensional gauged O(5) Skyrme models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4669-4683 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a family of four-dimensional nonlinear sigma models based on an O(5) symmetric group, whose fields take their values on the 4-sphere S4. An SO(4)-subgroup of the model is gauged. The solutions of the model are characterized by two distinct topological charges, the Chern–Pontryagin charge of the gauge field and the degree of the map, i.e., the winding number, of the S4 field. The one-dimensional equations arising from the variation of the action density subjected to spherical symmetry are integrated numerically. Several properties of the solutions thus constructed are pointed out. The only solution with unit Chern–Pontryagin charge are the usual BPST instantons with zero S4 winding number, while solutions with unit S4 winding number have zero Chern–Pontryagin charge. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1396636
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  • 7
    Electronic Resource
    Electronic Resource
    Finite energy–action solutions of p1 Yang–Mills equations on p2 Schwarzschild and deSitter backgrounds in dimensions d≥4 (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 5490-5509 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Physically relevant gauge and gravitational theories can be seen as special members of hierarchies of more elaborate systems. The Yang–Mills (YM) system is the first member of a hierarchy of Lagrangians which we will index by p1, and the Einstein–Hilbert (EH) system of general relativity is the first member of another hierarchy which we index by p2. In this paper, we study the classical equations of the p1=1,2 YM hierarchy considered in the background of special geometries (Schwarzschild, deSitter, anti-deSitter) of the p2=1,2,3 EH hierarchy. Solutions are obtained in various dimensions and lead to several examples of nonself-dual YM fields. When p1=p2 self-dual solutions exist in addition. Their action is equal to the Chern–Pontryagin charge and can be compared with that of the nonself-dual solutions. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533421
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  • 8
    Electronic Resource
    Electronic Resource
    Quommutator deformations of spl(N,1) (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4923-4927 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We analyze the Witten-Woronowicz's type deformations of the Lie superalgebras spl(N,1) and obtain deformations parametrized by N(N−1)/2 independent parameters for N〉2 and by three parameters for N=2. For some of these algebras, finite dimensional representations can be constructed in terms of finite difference operators, providing operators that are relevant for the classification of quasiexactly solvable, finite difference equations. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532499
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  • 9
    Electronic Resource
    Electronic Resource
    The structure of quasi-exactly solvable systems (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 4340-4349 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The linear, differential operators that preserve the N-dimensional vector space whose entries are polynomials of fixed, but arbitrary, degrees in one variable are considered herein. They are relevant for the classification of quasi-exactly solvable systems of equations. Generating elements are explicitly constructed and rules for ordering their products are derived. Some examples of equations that can be reduced to such systems are discussed. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530965
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  • 10
    Electronic Resource
    Electronic Resource
    Quasi-exactly-solvable system and sphaleron stability (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 2107-2114 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show explicitly that the eigenvalue equation describing the normal modes of the sphalerons in the 1+1 Abelian Higgs model is a quasi-exactly-solvable system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530159
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