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We develop a gauge-invariant linear response theory for relativisticBardeen-Cooper-Schrieffer (BCS) superfluids based on aconsistent-fluctuation-of-the order-parameter (CFOP) approach. The responsefunctions from the CFOP approach satisfy important generalized Ward identities.The gauge invariance of the CFOP theory is a consequence of treating the gaugetransformation and the fluctuations of the order parameter on equal footing socollective-mode effects are properly included. We demonstrate that the pole ofthe response functions is associated with the massless Goldstone boson.Important physical quantities such as the compressibility and superfluiddensity of relativistic BCS superfluids can also be inferred from our approach.We argue that the contribution from the massless Goldstone boson is crucial inobtaining a consistent expression for the compressibility.

Gauge Invariant Linear Response Theory of Relativistic BCS superfluids