Abstract
Based on the Ward–Takahashi identities representing both charge and velocity local conservation laws, we provide a scheme for constructing the vertex function Γˆ in the self-consistent iteration loop to determine the self-energy Σˆ for superconductivity. For a singlet superconductor without spin-dependent interaction, the relationship between Γˆ and Σˆ in this iteration loop is mainly controlled by the electronic compressibility of the system, which is directly related to the velocity of the Nambu-Goldstone mode.
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