Nonuniqueness of Kivelson, Kallin, Arovas and Schrieffer' fractional charge

TL;DR

This paper reveals that previous calculations of fractional charge in quantum systems are not unique due to improper treatment of magnetic length, leading to the disappearance of fractional charge in certain models.

Contribution

It demonstrates that the classical action calculation was flawed, showing that fractional charge results depend on the correct resolution of magnetic length and charge.

Findings

Fractional charge disappears when magnetic length is not correctly treated.

Kivelson et al's results are not unique due to this oversight.

Only the flux area becomes fractional, not the charge.

Abstract

It is found that the magnetic length has not been treated correctly to calculate the classical action. In fact, the charge and the magnetic length have not been resolved. It is of serious consequences because fractional charge completely disappears and only the flux area, $\l_o^2$ becomes fractional. The results of Kivelson et al are therefore not unique.