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