  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.
