Long-wave asymptotic behavior of the Green's functions of a mixture of superfluids

This paper obtains the exact form of the Green's functions of a mixture of superfluids in the long-wave limit with allowance for the infrared divergence of the field diagrams. The manifestations of the infrared anomaly are investigated in the case of a multi-component superfluid. The authors not that the macroscopic wave functions of the components are determined by the total number density of the particles and not by the superfluid component