Collective variables and composite fields

We consider use of collective variables for description of composite fields as collective phenomena due to the strong coupling regime. We discuss two approaches, where identification of collective variables of complex quantum system does not depend on knowledge of other degrees of freedom: (a) collective variables as parameters of group transformations changing the path integral of the system, and (b) collective variables as background fields for quantum system. In the case (a) we briefly present an approach. In the case (b) we consider fermions in an external scalar field, which serves as a collective variable in a nonlinear model for composite scalar field with a finite compositeness scale.