SU_M(2)timesU_C(1) Gauge Symmetry in High T_c Superconductivity

The square lattice structure of $CuO_2$ layers and the strongly correlated property of electrons indicate that the high $T_c$ superconductivity in cuprates can be described by a SO$_M$(5) coherent pairing state in which a SU$_M$(2)$\times$U$_C$(1) gauge symmetry is embedded. The spin and charge fluctuations that characterize the low energy magnetic excitations in cuprates are controlled by this intrinsic SU$_M$(2)$\times$U$_C$(1) gauge symmetry.