Asymmetric Bethe-Salpeter equation for pairing and condensation
The main purpose of the present paper is to re-examine the Martin-Schwinger hierarchical structure of correlations. The author investigates the binary collision approximation as well as three-particle correlations, which enable to derive the corresponding Bethe-Salpeter equations. Dependent on the considered channel the author obtains one complete-selfconsistent and one channel-dressed selfconsistent propagator. The binary collision approximation leads to one Hartree-Fock and one selfconsistent propagator in agreement with the Kadanoff and Martin form. This leads to the gap equation of pairing while the standard Bethe-Salpeter equation with two selfconsistent propagators does not. The proofs strongly rely on basic properties of Green functions.
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