  Classical and quantum theory of spin waves in the vortex state of a
mesoscopic sub-micron magnetic disk has been developed with account of the
finite mass density of the vortex. Oscillations of the vortex core resemble
oscillations of a charged string in a potential well in the presence of the
magnetic field. Conventional gyroscopic frequency appears as a gap in the
spectrum of spin waves of the vortex. The mass of the vortex has been computed
that agrees with experimental findings. Finite vortex mass generates a
high-frequency branch of spin waves. Effects of the external magnetic field and
dissipation have been addressed.

Mesoscale and Nanoscale Physics