Effective Action and Renormalization Group Flow of Anisotropic Superconductors

TL;DR

This paper derives the effective action for anisotropic superconductors without assuming rotational symmetry, leading to consistent gap equations and RG flow equations for the electron-electron interaction.

Contribution

It introduces a method to compute the effective action and RG equations for anisotropic superconductors without symmetry assumptions, extending previous approaches.

Findings

Derived the effective action for anisotropic superconductors.

Obtained RG flow equations for electron-electron potential.

Confirmed consistency with conventional gap equations.

Abstract

We calculate the effective action of a superconductor, without assuming that either the electron-electron potential or the Fermi surface obey rotational invariance. This approach leads to the same gap equation and equilibrium free energy as more conventional methods. The results are used to obtain the Gell-Mann - Low renormalization group equations for the electron-electron potential.