account the local character of interaction. The role of nonlocal interaction was recently discussed for ultracold Bose [@JPhysB; @JPhysB2] and Fermi [@Ferm-nonloc1; @Fermi-nonloc2] gases.

Finally, if the interaction Hamiltonian is SU(2) symmetric so that it contains the spin operators $S^{i}$ only, then the ferromagnetic state of spin-1 condensate is characterized by the following spectra of single-particle excitations [@APS; @PelPelSl]: $$\begin{gathered}
\omega_{{\bf p}}^{(1)}=\varepsilon_{\bf p}-2J(0)n+2h, \\
\omega_{{\bf p}}^{(2)}=\varepsilon_{\bf p}-n_{0}(J({\bf p})-J(0))+h, \\
\omega_{\bf p}^{(3)}=\left[\varepsilon_{\bf p}^{2}+2\varepsilon_{\bf p}n_{0}\left(U({\bf p})+J({\bf p })\right)\right]^{1/2}\end{gathered}$$ which are in agreement with other studies [@Ho; @Ohmi; @Ueda] if the interaction is taken to be of the contact type, $$U({\bf p})=U(0)={{g_{0}+2g_{2}}\over 3}, \quad J({\bf p})=J(0)={{g_{2}-g_{0}}\over 3},$$ with $g_{0}$ and $g_{2}$ being related to the s-wave scattering lengths of the total spin-1 channel [@Ueda].

Therefore, the extension of the Hamiltonian to SU(3) symmetry leads to the appearance of new description parameters (along with the magnetization vector) and changes the ground state and single-particle excitation spectra of ferromagnetic Bose-Einstein condensate.

Concluding remarks
==================

We have proposed a general approach for describing a many-body system of interacting spin-1 objects. It has been shown that the microscopic spin-1 objects inevitably induce both SU(3) symmetry of a many-body system and appearance of additional description parameters along with 