From second quantization to the BCS Hamiltonian

Under the conditions k ′+ k =0 and σ ′+ σ =0 one can straightforwardly derive the Bardeen–Cooper–Schrieffer (BCS) Hamiltonian from the second quantization Hamiltonian of a fermion system. The condition k ′+ k =0 can statistically be understood as a simplified mathematical summary of the fact that the total momentum of the fermion system is zero with respect to the center of mass. Based on the Pauli exclusion principle, the BCS Hamiltonian has been reinterpreted, in which V( k ′, k ) is understood as the interaction between an electron and a hole and naturally becomes attractive in the particle–hole channel without invoking phonons, while the interaction between two electrons or in the particle–particle channel is still repulsive other than attractive. With the reinterpretation and without the concept of Cooper's pairing, the BCS theory is found to remain valid for conventional superconductivity. It is thus suggested that the concept of Cooper's pairing be removed from superconductivity. By doing so many of the conflicts currently existing in the superconductivity community would automatically disappear. It is emphasized that the proposed reinterpretation is essential for unifying the description of low- and high-temperature superconductivity and further for developing a unified theory of superconductivity.