Dynamical Group SO(6) and Coexistence: Superconductivity and Charge-Density Waves

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Abstract
SO(6) is identified as the dynamical group of a mean-field Hamiltonian for the coexistence of superconductivity and charge-density waves. The energy spectrum is given in terms of the Casimir invariants. The explicit rotation of the Hamiltonian to canonical Cartan (diagonal) form is found, and expressions for the superconductivity and charge-density-wave order parameters are given in terms of the rotation angles. The descent from the SO(6) to the decoupled BCS-SO(3) and charge-density-wave-U(2) algebras is exhibited.