3 research outputs found
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