A geometrical derivation of the Dirac equation

We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice sites. Starting with a difference equation for the case of one spatial and one time dimensions, we generalize the approach to higher dimensions. Interactions with external electromagnetic and gravitational fields are also considered. One logical interpretation is that only at the lattice sites is the spin-1/2 particle aware of its mass and the presence of external fields.Comment: 9 pages, LaTeX, version accepted for publication in Phys. Lett.

Energy-momentum uncertainties as possible origin of threshold anomalies in UHECR and TeV-gamma ray events

A threshold anomaly refers to a theoretically expected energy threshold that is not observed experimentally. Here we offer an explanation of the threshold anomalies encountered in the ultra-high energy cosmic ray events and the TeV-gamma ray events, by arguing that energy-momentum uncertainties due to quantum gravity, too small to be detected in low-energy regime, can affect particle kinematics so as to raise or even eliminate the energy thresholds. A possible modification of the energy-momentum dispersion relation, giving rise to time-of-flight differences between photons of different energies from gamma ray bursts, is also discussed.Comment: minor changes in text and reference