Comment on " Topological phase in two flavor neutrino oscillations"

TL;DR

This paper critically examines claims about topological phases in neutrino oscillations, clarifying misconceptions and highlighting that the discussed phase is an artifact of approximations rather than a genuine topological phase.

Contribution

It clarifies the nature of the phase in neutrino oscillations, emphasizing that the claimed topological phase is an artifact and proposing a more robust phase interpretation.

Findings

The $$ phase is an artifact of approximations.

A more robust $$ phase exists as a Pancharatnam phase.

Distinction between geometric and topological phases clarified.

Abstract

We critically analyze the claims with regard to the relevance of topological phases in the physics of neutrino oscillation made in a recent paper [Phys. Rev. D 79, 096013 (2009)] and point out some inappropriate exaggerations and misleading statements. We find that the $\pi$ phase described in this paper, while interesting, is an artefact of two major approximations made in the paper. We point out a more robust and more familiar $\pi$ phase in the neutrino oscillation formulae which can be interpreted as a pure Pancharatnam phase. We also make some relevant remarks on the distinction between the geometric and the topological phase made in the commented paper.