## Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

We study the algebra Sp([ital n],[ital R]) of the symplectic model, in particular for the cases [ital n]=1,2,3, in a new way. Starting from the Poisson-bracket realization we derive a set of partial differential equations for the generators as functions of classical canonical variables. We obtain a solution to these equations that represents the classical limit of a boson mapping of the algebra. We show further that this mapping plays a fundamental role in the collective description of many-fermion systems whose Hamiltonian may be approximated by polynomials in the associated algebra, as is done in the simplest versions of themore »