In this talk, some aspects of the effective, or collective, description of
complex quantum systems within the path integral formalism are described.
In general, considering a generalisation of the standard Feynman-Vernon
Caldeira-Leggett model, an effective theory is obtained after "integrating
out" the environment. Depending on the environment and the choice of
coupling, a quantum theory of dissipation, or a coordinate-dependent mass
can be obtained. For the latter case, the proper discretisation of the
path integral is essential: we find that in general a simple effective
low-energy Hamiltonian, in which only the coordinate-dependent mass
enters, cannot be formulated. The quantum theory of weakly coupled
superconductors and the quantum dynamics of vortices in Josephson junction
arrays are examples where these considerations, in principle, are of
relevance.