In using spinor representation for the electron field, the charge density is given by a 2 × 2 matrix in the spin space. The propagator is also a 2 × 2 matrix. The diagonal term gives the usual many electron problem, and the off-diagonal term gives the superconductive state. The SCF equation for the usual many-electron problem turns out to be the gap equation for the superconductivity problem.
This treatment presents a new theory for the high temperature superconductivity by using the multi-band treatment from which the attractive electron-electron coupling is effectively derived. This coupling is electronic, but not phonon associated. The energy region for making superconductivity possible is a hundred times larger than the phonon frequency.