98 research outputs found
Self-Dual Vortices in Abelian Higgs Models with Dielectric Function on the Noncommutative Plane
We show that Abelian Higgs Models with dielectric function defined on the
noncommutative plane enjoy self-dual vorticial solutions. By choosing a
particular form of the dielectric function, we provide a family of solutions
whose Higgs and magnetic fields interpolate between the profiles of the
noncommutative Nielsen-Olesen and Chern-Simons vortices. This is done both for
the usual model and for the semilocal model with a
doublet of complex scalar fields. The variety of known noncommutative self-dual
vortices which display a regular behaviour when the noncommutativity parameter
tends to zero results in this way considerably enlarged
Low Energy Vortex Dynamics in Abelian Higgs Systems
The low energy dynamics of the vortices of the Abelian Chern-Simons-Higgs system is investigated from the adiabatic approach. The difficulties involved in treating the field evolution as motion on the moduli space in this system are shown. Another two generalized Abelian Higgs systems are discusssed with respect to their vortex dynamics at the adiabatic limit. The method works well and we find bound states in the first model and scattering at right angles in the second system
On an approach for computing the generating functions of the characters of simple Lie algebras
We describe a general approach to obtain the generating functions of the
characters of simple Lie algebras which is based on the theory of the quantum
trigonometric Calogero-Sutherland model. We show how the method works in
practice by means of a few examples involving some low rank classical algebras
Quantum trigonometric Calogero-Sutherland model, irreducible characters and Clebsch-Gordan series for the exceptional algebra E7
We re-express the quantum Calogero-Sutherland model for the Lie algebra E7
and the particular value of the coupling constant K=1 by using the fundamental
irreducible characters of the algebra as dynamical variables. For that, we need
to develop a systematic procedure to obtain all the Clebsch-Gordan series
required to perform the change of variables. We describe how the resulting
quantum Hamiltonian operator can be used to compute more characters and
Clebsch-Gordan series for this exceptional algebra.Comment: 37 pages, 1 figur
Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra E6
The quantum trigonometric Calogero-Sutherland models related to Lie algebras
admit a parametrization in which the dynamical variables are the characters of
the fundamental representations of the algebra. We develop here this approach
for the case of the exceptional Lie algebra E6.Comment: 17 pages, no figure
Quantum trigonometric Calogero-Sutherland model and irreducible characters for the exceptional algebra E8
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland
model for the Lie algebra E8 and coupling constant k=1 by using the fundamental
irreducible characters of the algebra as dynamical independent variables. Then,
we compute the second order characters of the algebra and some higher order
characters
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