Discrete Physics and the Dirac Equation

TL;DR

This paper reformulates the 1+1 Dirac equation in light cone coordinates, solving it exactly with finite differences, and offers interpretations via Feynman's Checkerboard and bit-strings, bridging physics and computational models.

Contribution

It introduces two novel forms of the Dirac equation in light cone coordinates and provides exact solutions, connecting quantum physics with discrete and computational frameworks.

Findings

Exact solutions to the 1+1 Dirac equation in two forms

Interpretation of solutions via Feynman's Checkerboard

Representation using bit-strings

Abstract

We rewrite the 1+1 Dirac equation in light cone coordinates in two significant forms, and solve them exactly using the classical calculus of finite differences. The complex form yields ``Feynman's Checkerboard''---a weighted sum over lattice paths. The rational, real form can also be interpreted in terms of bit-strings.