Abstract
The density fluctuation in a Bose gas interacting via a strong short-range repulsive potential and a weak long-range attractive potential is studied by the methods of quantum-field theory. The density-density correlation function is generated by taking the functional derivative of the single-particle matrix Green's function ${G}_{1}(1,2)$ with respect to an auxiliary scalar field. For ${G}_{1}(1,2)$, we use the Hartree approximation for the attractive potential and the Hartree-Fock approximation for the short-range repulsive potential. We show that the density fluctuation spectrum is identical to the Beliaev approximation for the single-particle excitation spectrum.
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