Asymmetric Bethe-Salpeter Equation for Pairing and Condensation |
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Authors: | Klaus Morawetz |
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Institution: | 1.Münster University of Applied Science,Steinfurt,Germany;2.International Institute of Physics (IIP),Natal,Brazil;3.Max-Planck-Institute for the Physics of Complex Systems,Dresden,Germany |
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Abstract: | The Martin-Schwinger hierarchy of correlations are reexamined and the three-particle correlations are investigated under various
partial summations. Besides the known approximations of screened, ladder and maximally crossed diagrams the pair-pair correlations
are considered. It is shown that the recently proposed asymmetric Bethe-Salpeter equation to avoid unphysical repeated collisions
is derived as a result of the hierarchical dependencies of correlations. Exceeding the parquet approximation we show that
an asymmetry appears in the selfconsistent propagators. This form is superior over the symmetric selfconsistent one since
it provides the Nambu-Gorkov equations and gap equation for fermions and the Beliaev equations for bosons while from the symmetric
form no gap equation results. The selfenergy diagrams which account for the subtraction of unphysical repeated collisions
are derived from the pair-pair correlation in the three-particle Green’s function. It is suggested to distinguish between
two types of selfconsistency, the channel-dressed propagators and the completely dressed propagators, with the help of which
the asymmetric expansion completes the Ward identity and is Φ-derivable. |
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Keywords: | |
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