23 research outputs found
Beyond fuzzy spheres
We study polynomial deformations of the fuzzy sphere, specifically given by
the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the
Poisson structure on a surface in . We find that several
surfaces, differing by constants, are described by the Higgs algebra at the
fuzzy level. Some of these surfaces have a singularity and we overcome this by
quantizing this manifold using coherent states for this nonlinear algebra. This
is seen in the measure constructed from these coherent states. We also find the
star product for this non-commutative algebra as a first step in constructing
field theories on such fuzzy spaces.Comment: 9 pages, 3 Figures, Minor changes in the abstract have been made. The
manuscript has been modified for better clarity. A reference has also been
adde
Aspects of coherent states of nonlinear algebras
Various aspects of coherent states of nonlinear and
algebras are studied. It is shown that the nonlinear Barut-Girardello
and Perelomov coherent states are related by a Laplace transform. We then
concentrate on the derivation and analysis of the statistical and geometrical
properties of these states. The Berry's phase for the nonlinear coherent states
is also derived.Comment: 22 Pages, 30 Figure