A Unified and Asymptotically Exact Theory of Superconductivity from Weak to Strong Coupling in an Electron–Phonon Model

Since the discovery of MgB₂, fundamental studies of the electronphonon mechanism have received intense interest. In this paper, starting from an electron–phonon model Hamiltonian, the third formalism of quantum statistics, and a diagonalization theorem, a unified and asymptotically exact theory of superconductivity is developed. The results are compared with those of McMillan, Allen and Dynes and experimental data. It is shown that the new results are in very good agreement with the experimental data. The unified theory has no extra assumptions and also supplies an exactly soluble example of the third formalism of quantum statistics. The T_c of MgB₂ is at a unified T_c line, the reason for the vacuum fluctuation mechanism are also discussed.