Theory of electrons with orbital degeneracy

The Hubbard model for electrons with orbital degeneracy is shown to have an underlying SU_d(4) symmetry of spin-orbital double. A hidden charge SU_c(4) symmetry is exposed and an extended Lieb-Mattis transformation which maps these two symmetries into each other is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a SO(6) Heisenberg magnet at half-filling and a SU(4) one at quarter-filling. The band is half-filled at all temperature for $\mu=3U/2$. The features of ground state and low-lying excitations in one dimension are indicated according to exact solutions. Various possibilities of symmetry breaking are also given.