  A new investigation of the coexistence and competition of ferroelectricity
and superconductivity is reported. In particular we show that the starting
Hamiltonian of a previous study by Birman and Weger (2001) can be exactly
diagonalized. The result differs significantly from mean-field theory. A
Hamiltonian with a different realization of the coupling between
ferroelectricity and superconductivity is proposed. We report the results for
mean-field theory applied to this Hamiltonian. We find that the order
parameters are strongly affected by this coupling.
