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The conserving approximation scheme due to Baym and Kadanoff (BK) provides
a fundamental algorithm for a quantitative treatment of the many-body effects
in the framework of the Green's-function method. Takada has noticed that
the repeated applications of the BK algorithm produce the exact solution
and thus this is regarded as the finding of a basic
prescription for
the exact self-energy [1].
Takada has also proposed a simplified version of the prescription using
the Ward identity and named it GISC
[2]. The usefulness of GISC together with the importance of the vertex
corrections is illustrated in the polaron problem [3,4]. Based on GISC,
Takada has embarked for the construction of a strong-coupling theory of
superconductivity with the vertex corrections included properly [5].
Takada and Hotta have obtained a concept of dynamical localization in the course of the investigation into the relation between GISC and the mean-field theory in infinite dimensions [7-9]. Currently, we are developing a method which goes beyond GISC. Employing the method, we begin with an intensive study on the microscopic mechanism of high-temperature superconductivity. |