Gauge invariance of the beta-function in nonrelativistic quantum electrodynamics

TL;DR

This paper demonstrates that in nonrelativistic quantum electrodynamics with a Fermi surface, the one-loop beta-function remains gauge-invariant for certain gauge choices, highlighting consistency in gauge theories applied to condensed matter systems.

Contribution

It proves gauge invariance of the one-loop beta-function in nonrelativistic QED for specific gauge choices, clarifying theoretical consistency in condensed matter applications.

Findings

Beta-function is gauge-independent at one-loop order for certain gauges.

Supports the consistency of gauge theories in condensed matter physics.

Provides a foundation for further nonperturbative studies.

Abstract

Recently there has been much interest in gauge theories applied to condensed matter physics. I show that for a system of nonrelativistic electrons coupled to a U(1) gauge field in the presence of a Fermi surface, the beta-function to one-loop order is, for a particular family of gauge-choices, independent of the gauge-choice.