Feynman’s Corner Rule; Quantum Propagation from Special Relativity

Feynman’s sum-over-paths prescription for the Dirac equation in a two dimensional spacetime can be formulated to give an unconventional view of the relationship between quantization and special relativity. By considering a local rule for the maintenance of Lorentz covariance in a discrete space, one is able to see the origin of Feynman’s rule and, taking a continuum limit at the last step, one obtains the Dirac propagator as a manifestation of special relativity, rather than a formal addition to it. In this route to the Dirac equation, the path-dependent phase of wavefunctions, relativistic or not, is a direct manifestations of path-dependent proper time.