132 research outputs found
On the solitons of the Chern-Simons-Higgs model
Several issues concerning the self-dual solutions of the Chern-Simons-Higgs
model are addressed. The topology of the configuration space of the model is
analysed when the space manifold is either the plane or an infinite cylinder.
We study the local structure of the moduli space of self-dual solitons in the
second case by means of an index computation. It is shown how to manage the
non-integer contribution to the heat-kernel supertrace due to the
non-compactness of the base space. A physical picture of the local coordinates
parametrizing the non-topological soliton moduli space arises .Comment: 27 pages, 3 figures, to appear in The European Physical Journal
On the derivatives of generalized Gegenbauer polynomials
We prove some new formulae for the derivatives of the generalized Gegenbauer
polynomials associated to the Lie algebra .Comment: 3 pages, no figures; submitted to Theor. Math. Phy
Explicit computations of low lying eigenfunctions for the quantum trigonometric Calogero-Sutherland model related to the exceptional algebra E7
In the previous paper math-ph/0507015 we have studied the characters and
Clebsch-Gordan series for the exceptional Lie algebra E7 by relating them to
the quantum trigonometric Calogero-Sutherland Hamiltonian with coupling
constant K=1. Now we extend that approach to the case of general K
One-loop mass shift formula for kinks and self-dual vortices
A formula is derived that allows us to compute one-loop mass shifts for kinks
and self-dual Abrikosov-Nielsen-Olesen vortices. The procedure is based in
canonical quantization and heat kernel/zeta function regularization methods.Comment: LaTex file, 8 pages, 1 figure . Based on a talk given by J. M. G. at
the 7th Workshop on Quantum Field Theory under the Influence of External
Conditions (QFEXT05), Barcelona, Spain. Minor corrections. Version to appear
in Journal of Physics
Quantum corrections to the mass of self-dual vortices
The mass shift induced by one-loop quantum fluctuations on self-dual ANO
vortices is computed using heat kernel/generalized zeta function regularization
methods.Comment: 4 pages RevTex, version to appear in Physical Review
Quantum fluctuations around low-dimensional topological defects
In these Lectures a method is described to analyze the effect of quantum
fluctuations on topological defect backgrounds up to the one-loop level. The
method is based on the spectral heat kernel/zeta function regularization
procedure, and it is first applied to various types of kinks arising in several
deformed linear and non-linear sigma models with different numbers of scalar
fields. In the second part, the same conceptual framework is constructed for
the topological solitons of the planar semilocal Abelian Higgs model, built
from a doublet of complex scalar fields and one U(1) gauge field.Comment: 63 pages, 14 figures, expanded version of two lectures given by
J.M.G. in 5th International School on Field Theory and Gravitation, Cuiaba,
Brazi
Quantum oscillations of self-dual Abrikosov-Nielsen-Olesen vortices
The mass shift induced by one-loop quantum fluctuations on self-dual ANO
vortices is computed using heat kernel/generalized zeta function regularization
methods. The quantum masses of super-imposed multi-vortices with vorticity
lower than five are given. The case of two separate vortices with a quantum of
magnetic flux is also discussed.Comment: RevTex, 13 pages, 4 figures, 7 tables. Minor corrections. Version to
appear in Physical Review
Spectral Flow of Vortex Shape Modes over the BPS 2-Vortex Moduli Space
The flow of shape eigenmodes of the small fluctuation operator around BPS
2-vortex solutions is calculated, as a function of the intervortex separation
. For the rotationally-invariant 2-vortex, with , there are three
discrete modes; the lowest is non-degenerate and the upper two are degenerate.
As increases, the degeneracy splits, with one eigenvalue increasing and
entering the continuous spectrum, and the other decreasing and asymptotically
coalescing with the lowest eigenvalue, where they jointly become the eigenvalue
of the 1-vortex radial shape mode. The behaviour of the eigenvalues near
is clarified using a perturbative analysis, and also in light of the 2-vortex
moduli space geometry.Comment: 12 pages, 8 figure
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