  The method for calculating the ground-state energy and the optical
conductivity spectra is developed for a system of a finite number of
interacting arbitrary-coupling polarons in a spherical quantum dot with a
parabolic confinement potential. The path-integral formalism for identical
particles is used in order to take into account the fermion statistics. Using a
generalization of the Jensen-Feynman variational principle, the ground-state
energy of a confined N-polaron system is analyzed as a function of N and of the
electron-phonon coupling strength. The calculated optical conductivity spectra
of the N-polaron system in a quantum dot manifest features related to
ground-state transitions between states with different total spin.
