Comment on: "Quantum aspects of the Lorentz symmetry violation on an electron in a nonuniform electric field'' Eur. Phys. J. Plus (2020) 135:623

TL;DR

This paper critiques a recent study on Lorentz symmetry violation effects on electrons, arguing that its conclusions are artifacts of an approximation method and lack physical significance.

Contribution

It provides a critical analysis showing that previous results on Lorentz symmetry violation effects are due to an unphysical truncation in the mathematical expansion.

Findings

The supposed angular frequencies are artifacts of the approximation.

The conclusions of the original paper are unphysical and not valid.

The analysis clarifies the mathematical limitations in studying Lorentz violation effects.

Abstract

We analyze recent results concerning the hypothesis of a privileged direction in the space-time that is made by considering a background of the Lorentz symmetry violation determined by a fixed spacelike vector field and the analysis of quantum effects of this background on the interaction of a nonrelativistic electron with a nonuniform electric field produced by a uniform electric charge distribution. We show that the conclusions derived by the authors are an artifact of the truncation of the Frobenius series by means of the tree-term recurrence relation for the expansion coefficients. Thus, the existence of allowed angular frequencies stemming from this procedure is meaningless and unphysical.