Feynman's checkerboard: an elementary mathematical model in quantum theory

The course is devoted to the most elementary model of electron
motion suggested by R.Feynman. It is game, in which a checker moves on a checkerboard by certain simple rules, and we count the turnings. It turns out that this simple combinatorial model demonstrates visually many basic ideas of quantum theory.

If the lattice step tends to zero, then the model reproduces known experimental and theoretical results: for example, the percentage of light reflected by a thin film, or the probability to find an electron in a given place, if it was emitted from the origin and moves in a fixed plane. This is a purely mathematical course, where all assertions are stated and proved in a mathematical level of rigor. For mathematicians, it can be interesting in itself as a subject from (asymptotic) combinatorics. Those who are going to study quantum theory later, could recognize numerous analogies with the model. 

To attend the course, knowledge of school-level mathematics is sufficient; no prerequisites in physics are assumed. In particular, the course is accessible for 1st year students. 
Many results are suggested as problems for one's own solution.


1. Feynman's checkerboard: the simplest model of electron motion. Double-slit experiment. Dirac's equation on a 2-dimensional lattice. Spin. Charge. Mass. Convergence of Feynman's checkerboard to Dirac's theory. Source. Medium. Wave propagation. Dispersion relation. Thin film reflection. 

2. Extensions of Feynman's checkerboard. External electromagnetic field. Spin `precession'. Gauge transformations. Curvature. Charge conservation. Identical particles. Exclusion principle. Antiparticles. What is QED


Feynman, Richard (2006). QED: The strange theory of light and matter. Princeton University Press. ISBN 0-691-12575-9.