3,598 research outputs found
Vassiliev knot invariants and Chern-Simons perturbation theory to all orders
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
, and several minor changes. 31 pages, 19 figures, epsf.sty, Late
Quantum Loop Modules and Quantum Spin Chains
We construct level-0 modules of the quantum affine algebra \Uq, as the
-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
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
Using numerical arguments we find that for = 306 a tetrahedral
configuration () and for N=542 a dihedral configuration () are likely
the global energy minimum for Thomson's problem of minimizing the energy of
unit charges on the surface of a unit conducting sphere. These would be the
largest 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 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 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 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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