We examine the spectrum of small perturbations around global and local
(gauge) abelian vortices, using simple numerical matrix techniques. The results
are of interest for both cosmic strings and for their condensed matter
analogues, superfluid and superconducting vortices. We tabulate the
instabilities of higher winding number vortices, and find several bound states.
These localised oscillations of the order parameter can be thought of as
particle states trapped in the core of the string.Comment: Latex, 20 pages, 6 uuencoded figure
