Gauge Invariant Linear Response Theory of Relativistic BCS superfluids

TL;DR

This paper develops a gauge-invariant linear response theory for relativistic BCS superfluids, ensuring physical consistency and including collective modes, with implications for physical quantities like compressibility and superfluid density.

Contribution

It introduces a CFOP approach that maintains gauge invariance and properly accounts for collective modes in relativistic BCS superfluids, which was not previously achieved.

Findings

Response functions satisfy generalized Ward identities

Goldstone boson pole is identified as a massless mode

Goldstone boson contribution is essential for correct compressibility

Abstract

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