# Collective modes and restoration of gauge invariance in superconductivity

 P: 102 I'm not really qualified to answer your questions but maybe some references might help you on your way. If you are quite familiar with the functional integral approach then I think this is the more modern approach to dealing with superconductors in a gauge invariant manner as well as identifying the collective modes. See for example this article by van Otterlo, Golubev, Zaikin and Blatter, where they also discuss ward identities. Another pedagogical description can be found in Altland and Simons book Condensed Matter Field Theory. I think the connection to the dressed vertices might be found from the vertex generating functional (or effective potential) $\Gamma[\Psi]$ ($\Psi$ being the pairing field) that one can obtain with the functional integral technique (for definition and introduction see for example sec. 2.4 in Negele and Orland's book Quantum Many-Particle Systems). In Weinberg's book The quantum theory of fields Vol II you can find a treatment of superconductors in terms of the effective potential. Also see this article by Weinberg. I hope this helps in some way. Let me know if it was useful or if you find any more pedagogical references.