  The effective actions for both local and global curved vortices are derived,
based on the derivative expansion of the corresponding field theoretic actions
of the nonrelativistic Abelian Higgs and Goldstone models. The role of
excitations of the modulus and the phase of the scalar field and of the gauge
field (the Bogolyubov-Anderson mode) emitted and reabsorbed by vortices is
elucidated. In case of the local (gauge) magnetic vortex, they are necessary
for cancellation of the long distance divergence when using the transverse form
of the electric gauge field strength of the background field. In case of global
vortex taking them into account results in the Greiter-Wilczek-Witten form of
the effective action for the Goldstone mode. The expressions for transverse
Magnus-like force and the vortex effective mass for both local and global
vortices are found. The equations of motion of both type of vortices including
the terms due to the field excitations are obtained and solved in cases of
large and small contour displacements.
