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Memorial Conference on Analytic Number Theory and Applications Dedicated to the 130th Anniversary of I. M. Vinogradov
September 14, 2021 10:30–11:00, Moscow, Steklov Mathematical Institute, 8, Gubkina str, room 110 + online
 


Feynman Checkers: Number Theory in Quantum Electrodynamics

A. V. Ustinova, M. B. Skopenkovb

a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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A. V. Ustinov, M. B. Skopenkov


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Abstract: In the 40s, R. Feynman developed the simplest model of electron motion, now known asFeynman checkers. In this game, the checker moves around the chessboard according to simple rules and as a result describes the quantum-mechanical behavior of the electron. This model is also known as one-dimensional quantum walk or Ising model with imaginary temperature. We solve mathematically a problem by R. Feynman from 1965, which was to prove that the model reproduces the usual quantum-mechanical free-particle kernel for large time, small average velocity, and small lattice step. The main tools are the Fourier transform and the stationary phase method.

A more detailed description of the model and known results can be found in [1].

[1] M. Skopenkov, A. Ustinov, Feynman checkers: towards algorithmic quantum theory // arXiv:2007.12879 [math-ph] (2020).

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