After the first explanation of superconductivity by Bardeen, Cooper and Schrieffer, it was for several years a matter of concern to render the theory charge conserving and gauge invariant. I have been reading the article by Y. Nambu, Phys. Rev. Vol. 117, p. 648 (1960) who uses Ward identities to establish gauge invariance and the book by Schrieffer, "Theory of superconductivity" from 1964.(adsbygoogle = window.adsbygoogle || []).push({});

While I can follow the steps of the calculation, the physical content is not quite clear to me.

While the difference between a free and a "dressed" Greens function is quite clear to me, the

concept of a dressed vertex is much less. I only see it as a formal device to calculate the current-current correlation functions. The collective modes somehow fall out as homogeneous solutions of a Bethe Salpeter type equation.

Schrieffer stresses that the mechanism in fact is not peculiar to superconductivity but holds also in normal metals. I know of some discussions of the "backflow" which is also not too clear to me. I suppose that these matters are better understood now half a century later. Maybe someone knows a more pedagogical reference?

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# Collective modes and restoration of gauge invariance in superconductivity

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