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It is well-known fact that the appearance of superconducting state in superconductor relates to the existence of the pole in two-particle Green function.

Does exist a similar fact for Bose condensation?

I mean the following: one can compute a Green function of interacting Bose gas and see that a singularity of this function corresponds to appearance of condensate state

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Bose-Einstein condensation is not caused by interaction: ideal Bose gas undergo Bose-Einstein condensation. In contrast, superfluidity is due to interaction and one should see its signature in Green functions as a pole associated to phonons.

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