Comment on "Noncommutativity as a Possible Origin of the Ultrahigh-energy Cosmic Ray and the TeV Photon Paradoxes"

TL;DR

This paper critiques a proposed Lorentz-noninvariant dispersion law from noncommutative theory, showing it leads to tachyonic issues and photon instability, thus invalidating its explanation for ultrahigh-energy cosmic ray and TeV-photon anomalies.

Contribution

It provides a critical analysis demonstrating that the proposed dispersion law is inconsistent with physical stability and does not derive from the claimed theoretical framework.

Findings

The dispersion law does not follow from deformed oscillator systems.

The proposed law causes tachyonic propagation and photon instability.

It invalidates the law as an explanation for cosmic ray and TeV-photon anomalies.

Abstract

A Lorentz-noninvariant modification of the kinematic dispersion law was proposed in [hep-th/0211237], claimed to be derivable from from q-deformed noncommutative theory, and argued to evade ultrahigh energy threshold anomalies (trans-GKZ-cutoff cosmic rays and TeV-photons) by raising the respective thresholds. It is pointed out that such dispersion laws do not follow from deformed oscillator systems, and the proposed dispersion law is invalidated by tachyonic propagation, as well as photon instability, in addition to the process considered.