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Asymmetric Bethe-Salpeter Equation for Pairing and Condensation

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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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Authors and Affiliations

  1. Münster University of Applied Science, Stegerwaldstrasse 39, 48565, Steinfurt, Germany

    Klaus Morawetz

  2. International Institute of Physics (IIP), Av. Odilon Gomes de Lima 1722, 59078-400, Natal, Brazil

    Klaus Morawetz

  3. Max-Planck-Institute for the Physics of Complex Systems, 01187, Dresden, Germany

    Klaus Morawetz

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  1. Klaus Morawetz
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Correspondence to Klaus Morawetz.

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Morawetz, K. Asymmetric Bethe-Salpeter Equation for Pairing and Condensation. J Stat Phys 143, 482–500 (2011). https://doi.org/10.1007/s10955-011-0186-y

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  • DOI: https://doi.org/10.1007/s10955-011-0186-y

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