  We introduce a topological gauge vector potential which influences spin wave
excitations over arbitrary non-uniform, slowly moving magnetization
distribution. The time-component of the gauge potential plays a principal role
in magnetization dynamics, whereas its spatial components can be often
neglected for typical magnetic nanostructures. As an example, we consider spin
modes excited in the vortex state magnetic dots. It is shown that the vortex/
spin wave interaction can be described as a consequence of the gauge field
arising due to non uniform moving vortex magnetization distribution. The
coupled equations of motion of the vortex and spin waves are solved within
small excitation amplitude approximation. The model yields a giant frequency
splitting of the spin wave modes having non-zero overlapping with the vortex
mode as well as a finite vortex mass of dynamical origin.
