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

The effective action and equations of motion of curved local and global vortices: Role of the field excitations