Ground-state energy of the spinor Bose-Einstein condensate

It is known that for a weakly interacting Bose-Einstein condensate (BEC), t he assumption of a two-body delta interaction described by a constant coupl ing strength gives rise to a divergent ground-state energy. A similar diver gence occurs in the spinor condensate in which the spin-spin interaction is included in addition to the repulsive delta interaction. In this paper, we examine, in the standard Bogoliubov approximation, the ground-state energy of a homogeneous spinor BEC with hyperfine spin f = 1. The renormalized co upling constants an calculated and expressed in terms of the bare ones usin g the standard second-order perturbation method. With these renormalized co upling constants, we show that the ultraviolet divergence of the ground-sta te energy can be exactly eliminated. [S1050-2947(99)01106-3].