It is proposed to introduce a new type of effective Lagrangian for slow motion in the study of nuclear collective motion, resulting from the realization that gauge fields can be dynamically generated in traditional nuclear models. Berry's observation that under certain conditions the wave function of a "fast" subsystem acquires a geometrical phase in a cyclic evolution in fact implies that magnetic forces appear in the effective Hamiltonian of the collective degrees of freedom. Other topics of study include the theory of large amplitude collective motion, generalization of the Bogoliubov quasiparticle notion, pair properties of nuclei near nucleon drip lines, nonlocal equations and their local equivalent.