, Volume 20, Issue 7, pp 491-501

Feynman's relativistic chessboard as an ising model

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Abstract

Feynman has described a chessboard model for a one-dimensional relativistic quantum problem which yields the correct kernel for a free spin-1/2 particle moving in one spatial dimension. This chessboard problem can be solved as an Ising model, using the transfer matrix technique of statistical mechanics. The 2×2 transfer matrix represents the infinitesimal time evolution operator for the two eigenstates of the velocity operator.