Collective coordinates in Fermi systems

The problem of developing a consistent perturbation theory for a Fermi system in the case in which the unperturbed system exhibits dynamical symmetry breaking is discussed, by using collective coordinate methods. By adapting to this problem the methods used in the quantization of gauge theories, it is shown how to deal with composite zero-frequency excitations in such a way that the resulting perturbation theory is free of infrared divergencies. Explicit calculations are carried out in the case of a simple quantum mechanical model representing a superfluid Fermi system.