ua nt - p h / 99 11 10 8 v 1 2 5 N ov 1 99 9 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. Introduction In absence of particle-creation interaction, to describe a composite field means to solve the Schroedinger equation for constituent particles. When interaction changes particle number, one should work in the Fock space , and if coupling is strong , even a single particle should be described in the Fock space by the column vector with many rows; a single particle becomes ”dressed”. A composite particle state in the Fock space will include rows corresponding to different ways of combining indefinite many more elementary systems into states with the same internal quantum numbers. In Quantum Field Theory, this situation can be also expressed in language of the Bethe-Salpeter ∗to be published in the Proceedings of the Conference ”Probability and Irreversibility in Quantum Mechanics”, 5-9 July 1999, Fondation des Treilles, France This work was supported in part by RFBR (Grant 97-01-01186) and by GRACENAS (Grant 97-0-14.1-61).