3,575 research outputs found

    Vassiliev knot invariants and Chern-Simons perturbation theory to all orders

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    At any order, the perturbative expansion of the expectation values of Wilson lines in Chern-Simons theory gives certain integral expressions. We show that they all lead to knot invariants. Moreover these are finite type invariants whose order coincides with the order in the perturbative expansion. Together they combine to give a universal Vassiliev invariant.Comment: Revised version, includes a detailed proof of formula (5.26) for log⁡Z\log Z, and several minor changes. 31 pages, 19 figures, epsf.sty, Late

    Quantum Loop Modules and Quantum Spin Chains

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    We construct level-0 modules of the quantum affine algebra \Uq, as the qq-deformed version of the Lie algebra loop module construction. We give necessary and sufficient conditions for the modules to be irreducible. We construct the crystal base for some of these modules and find significant differences from the case of highest weight modules. We also consider the role of loop modules in the recent scheme for diagonalising certain quantum spin chains using their \Uq symmetry.Comment: 32 pages, 5 figures (appended), ENSLAPP-L-419/93, MRR2/9

    Plasma resonance radiation

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    Qualitative determination of charged particle cloud motion through corona and excitation of electron plasma oscillations through analysis of test particle electromagnetic field in plasm

    New Global Minima for Thomson's Problem of Charges on a Sphere

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    Using numerical arguments we find that for NN = 306 a tetrahedral configuration (ThT_h) and for N=542 a dihedral configuration (D5D_5) are likely the global energy minimum for Thomson's problem of minimizing the energy of NN unit charges on the surface of a unit conducting sphere. These would be the largest NN by far, outside of the icosadeltahedral series, for which a global minimum for Thomson's problem is known. We also note that the current theoretical understanding of Thomson's problem does not rule out a symmetric configuration as the global minima for N=306 and 542. We explicitly find that analogues of the tetrahedral and dihedral configurations for NN larger than 306 and 542, respectively, are not global minima, thus helping to confirm the theory of Dodgson and Moore (Phys. Rev. B 55, 3816 (1997)) that as NN grows dislocation defects can lower the lattice strain of symmetric configurations and concomitantly the energy. As well, making explicit previous work by ourselves and others, for N<1000N<1000 we give a full accounting of icosadeltahedral configuration which are not global minima and those which appear to be, and discuss how this listing and our results for the tetahedral and dihedral configurations may be used to refine theoretical understanding of Thomson's problem.Comment: 1- Manuscript revised. 2- A new global minimum found for a dihedral (D_5) configuration found for N=54
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