Self-consistent symmetries of the Hartree-Fock-Bogoliubov equations in a rotating frame

The self-consistent symmetries σ_x (reflection through the yz plane) and TR_z(π) and their eigenfunctions are employed to reduce the dimension of the Hartree-Fock-Bogoliubov equations in a rotating frame by a factor of two. In the canonical or BCS representation, σ_x, maps each single-particle orbital into itself.