Vertex correction and Ward identity in the U(1) gauge theory with Fermi surface

TL;DR

This paper demonstrates that including vertex corrections in a self-consistent ladder approximation does not alter the fundamental dynamics of spinons and gauge fluctuations in a U(1) gauge theory with a Fermi surface.

Contribution

It shows that vertex corrections do not change the dynamics in the U(1) gauge theory with Fermi surface within the ladder approximation.

Findings

Vertex corrections do not modify the dynamics of spinons.

Gauge fluctuations remain unaffected by vertex corrections.

Self-consistent ladder approximation is robust against vertex corrections.

Abstract

We show that introduction of vertex corrections in the fully self-consistent ladder approximation does not modify dynamics of spinons and gauge fluctuations in the U(1) gauge theory with Fermi surface.