Number-conserving mean-field theory for Bose-Einstein condensates

I formulate a mean-field theory of Bose-Einstein condensation based on numb er-conserving many-body theory. I use techniques commonly adopted in nuclea r structure theories to derive the mean-field equations. I compare my formu lation with the Bogoliubov approach and I emphasize the key role played by the zero-energy eigenmode when we contrast these two approaches. The differ ences with analogous previous formulation are also pointed out.