Waves on Noncommutative Spacetime and Gamma-Ray Bursts

TL;DR

This paper explores wave phenomena on noncommutative spacetime using quantum group Fourier transforms, predicting potentially observable dispersion effects in gamma-ray bursts and proposing new field theory constructions with CPT violation implications.

Contribution

It introduces a wave equation on noncommutative Minkowski spacetime and a novel approach to field theories incorporating noncommutativity and non-Abelian momentum addition.

Findings

Predicted large dispersion effects in gamma-ray bursts for Planck-scale noncommutativity.

Outlined a new framework for field theories on noncommutative spacetime.

Suggested possible CPT violation effects detectable in neutral-kaon experiments.

Abstract

Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime $[x^i,t]=\imath\lambda x^i$. A natural wave equation is derived and the associated phenomena of {\it in vacuo} dispersion are discussed. Assuming the deformation scale $\lambda$ is of the order of the Planck length one finds that the dispersion effects are large enough to be tested in experimental investigations of astrophysical phenomena such as gamma-ray bursts. We also outline a new approach to the construction of field theories on the noncommutative spacetime, with the noncommutativity equivalent under Fourier transform to non-Abelianness of the `addition law' for momentum in Feynman diagrams. We argue that CPT violation effects of the type testable using the sensitive neutral-kaon system are to be expected in such a theory.