Ward identities for strongly coupled Eliashberg theories

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We discuss Ward identities for strongly interacting fermion systems described by Eliashberg-type theories. We show that Ward identities are not in conflict with the Migdal theorem and derive diagrammatically a Ward identity for a charge vertex both in a Fermi liquid and when a Fermi liquid is destroyed at quantum criticality. We argue that a Ward identity for the spin vertex cannot be obtained within the Eliashberg theory.

Original languageEnglish (US)
Article number085113
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number8
StatePublished - Aug 15 2005


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