Abstract
An effective Hamiltonian with auxiliary bosons and auxiliary fermions is proposed to treat the Hubbard Hamiltonian with strong correlation. Auxiliary particles themselves can not describe any real excitations. In particular, the Bose condensation of auxiliary bosons never occurs, and auxiliary fermions have no Fermi surfaces. Real excitations are described by two kinds of pair-excitations of auxiliary particles, such as fermionic and bosonic pair-excitations. Superconductivity in the effective Hamiltonian is nothing but the condensation of Cooper pairs between fermionic pair-excitations, which are formed by the superexchange interaction mediated by auxiliary fermions. The proposed model of superconductivity is consistent with anisotropic-singlet superconductivity previously examined by the present author (Jpn. J. Appl. Phys. 26 (1987) L652.), which is based on the Fermi liquid theory of the Hubbard Hamiltonian.
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