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Ward identities for strongly coupled Eliashberg theories

Andrey V. Chubukov
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Abstract

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

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Andrey V. Chubukov. 2004-11-01. Ward identities for strongly coupled Eliashberg theories. https://doi.org/10.1103/physrevb.72.085113

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