Waves on noncommutative space-time and gamma-ray bursts

Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski space-time [x(i),t] = i lambdax(i). A natural wave equation is derived and the associated phenomena of 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 space-time, 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.