Comment on "Dynamic correlations of the spinless Coulomb Luttinger liquid [Phys. Rev. B {\bf 65}, 125109 (2002)]"

TL;DR

This paper critiques a previous study on Coulomb Luttinger liquids, arguing that its mathematical analysis was flawed and that its conclusions about dynamical correlations are probably incorrect.

Contribution

It provides a critical review and correction of the mathematical analysis and conclusions in the prior work on Coulomb Luttinger liquids.

Findings

Previous claims about threshold behavior are based on inconsistent analysis

Physical arguments suggest the claimed behavior is unlikely to be correct

Highlights the importance of correct mathematical treatment in Luttinger liquid studies

Abstract

We show that claims, presented in Phys. Rev. B {\bf 65}, 125109 (2002) concerning the threshold behavior of dynamical correlations of a Coulomb Luttinger liquid, are based on an inconsistent mathematical analysis. Physical arguments are also presented, indicating that the claimed behavior is unlikely to be correct.