Feynman checkers: through the looking-glass

TL;DR

This paper rigorously formalizes Feynman's elementary quantum theory model using mathematical tools, deriving optical formulas and connecting to quantum walks and the six-vertex model.

Contribution

It introduces a rigorous mathematical framework for Feynman's elementary quantum model, linking it to advanced mathematical tools and other quantum models.

Findings

Accurate quantitative results for the Feynman checker model

Derivation of a well-known optical formula

Connection to quantum walks and six-vertex model

Abstract

Feynman gave a famous elementary introduction to quantum theory by discussing the thin-film reflection of light. We make his discussion mathematically rigorous, keeping it elementary, using his other idea. The resulting model leads to accurate quantitative results and allows us to derive a well-known formula from optics. In the process, we get acquainted with mathematical tools such as Smirnov's fermionic observables, transfer matrices, and spectral radii. Quantum walks and the six-vertex model arise as the next step in this direction.