The superconducting phase transition and gauge dependence

TL;DR

This paper investigates the gauge dependence of the superconducting phase transition in the Ginzburg-Landau model, showing that the critical exponent for the order parameter is gauge independent in three dimensions, with analysis in different theoretical frameworks.

Contribution

It demonstrates the gauge independence of the superconducting order parameter exponent using Ward-Takahashi identities and compares different approaches in the context of gauge choices.

Findings

The exponent $eta$ is gauge independent in 3D.

Landau gauge has a special physical meaning in 3D.

Differences in gauge dependence arise between $oldsymbol{ extepsilon}$-expansion and fixed dimension approaches.

Abstract

The gauge dependence of the renormalization group functions of the Ginzburg-Landau model is investigated. The analysis is done by means of the Ward-Takahashi identities. After defining the local superconducting order parameter, it is shown that its exponent $\beta$ is in fact gauge independent. This happens because in $d=3$ the Landau gauge is the only gauge having a physical meaning, a property not shared by the four-dimensional model where any gauge choice is possible. The analysis is done in both the context of the $\epsilon$-expansion and in the fixed dimension approach. It is pointed out the differences that arise in both of these approaches concerning the gauge dependence.