Self-consistent description of superconductivity in the crystal lattice

The generalized system of self-consistent Hartree-Fock-Bogolubov (HFB) equations at finite temperatures for the conduction electrons in solid is obtained. The spatial symmetry of crystal lattice is taken into account. The equations describe the magnetic properties of electrons as well as possibility of their transitions into the singlet or triplet superconducting states. The symmetry properties of the nonlinear HFB equations are investigated with respect to the space group and time-reversal transformations. It is shown that the inclusion of electron-electron interaction does not change the classification of electron states, which is used in the one-electron approach.