Global $SO(3)\times SO(3)\times U(1)$ symmetry of the Hubbard model on bipartite lattices

It is found that for on-site interaction $U\mathrm{\ne }0$ the local $SU(2)\times SU(2) \times U(1)$ gauge symmetry of the Hubbard model on a bipartite lattice with vanishing transfer integral $t=0$ can be lifted to a global $[SU(2)\times SU(2)\times U(1)]/Z_2^2=SO(3)\times SO(3)\times U(1)$ symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with $t>0$. The generator of the new found hidden independent charge global U(1) symmetry is one half the rotated-electron number of singly-occupied sites operator. It is confirmed elsewhere that our results have important physical consequences concerning the further understanding of the unusual properties of the hole-doped cuprates.