Simple condensation of composite bosons in a number conserving approach to many fermion-systems

We recently proposed an exact bosonization procedure which generates a Hamiltonian of composite bosons interacting among themselves and with fermionic quasiparticles. The interaction among composites whose mixing is allowed by symmetries is strong, but a simple condensate cannot have a significant mixing with other composites. We determine the conditions of decoupling, study their effects and compare the results with the Random Phase Approximation and the BCS theory.