Abstract
Abstract The filed-theoretic analysis of Wong and Gould for a Bose fluid is used to study response functions at arbitrary temperatures. Several rigorous identities are derived for density and momentum current response functions in the high- and low-frequency limits. These involve the condensate fraction n 0 and the superfluid density ϱ s . By explicit calculations using the one-loop diagrammatic approximation for the proper irreducible functions, these rigorous results are verified at finite temperatures. In particular, the zero-frequency Gavoret-Nozieres relation, the high-frequency Wong-Gould f -sum rule, and the impulse approximation at high momentum transfers are all satisfied in this simple microscopic calculation. On the other hand, the superfluid f -sum rule is found not to be satisfied.
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