December 16, 2019. M. B. Skopenkov (NRU Higher School of Economics, Institute for Information Transmission Problems RAS). The Feynman checkerboard: discrete quantum mechanics (joint work with A. Ustinov).

We study the most elementary model of electron motion introduced by R.Feynman. It is a game, in which a checker moves on a checkerboard by simple rules, and we count the turnings. We give a first rigorous proof that the continuum limit of the model reproduces the retarded Green function for the (1+1)-dimensional Dirac equation, and provide an explicit estimate for the convergence rate. This justifies a heuristic derivation by J.Narlikar from 1972. In a sense, this is also a continuum limit of a 1-dimensional Ising model at imaginary temperature (H.Gersch, 1981), and a new approach to making quantum field theory rigorous and algorithmic. For the model, we also show an exact charge conservation and a coupling to lattice gauge theory, and state visual open problems.

Most of the talk is accessible to undergraduate students; no knowledge of physics is assumed.

The work was prepared within the framework of the Academic Fund Program at the National Research University Higher School of Economics (HSE) in 2018-2019 (grant N18-01-0023) and by the Russian Academic Excellence Project ``5-100''.

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