Exactly solvable pairing models inspired by high-T_c superconductivity
The BCS theory models electron correlations with pure zero-momentum pairs. I consider a family of pairing Hamiltonians, where the electron correlations are modelled with pure arbitrary-momentum pairs. I present exact solutions to this family. The BCS pairing, the \eta pairing and the d -wave pairing in T_c superconductivity are the family members. These models, expect for the BCS model, are legitimate only on an xy plane defined by the electron spin S_z, compatible with the two dimensionality of high temperature superconductivity. Surprisingly, all parings are on equal footing in the xy plane, suggesting a unification of the s-wave and d-wave theoretical mechanisms in high T_c superconductivity. I also give the extension that includes all members of this family.