Feynman Checkerboard - History

History

Feynman invented the model in the 1940s while developing his spacetime approach to quantum mechanics. He did not publish the result until it appeared in a text on path-integrals coauthored by Albert Hibbs in the mid 1960s. The model was not included with the original path-integral paper because a suitable generalization to a four dimensional spacetime had not been found.

One of the first connections between the amplitudes prescribed by Feynman for the Dirac particle in 1+1 dimensions, and the standard interpretation of amplitudes in terms of the Kernel or propagator, was established by Narlikar in a detailed analysis. The name 'Feynman Chessboard Model' was coined by Gersch when he demonstrated its relationship to the one-dimensional Ising model. Gaveau et al. discovered a relationship between the model and a stochastic model of the Telegraph equations due to Mark Kac through analytic continuation. Jacobson and Schulman examined the passage from the relativistic to the non-relativistic path integral. Subsequently Ord showed that the Chessboard model was embedded in correlations in Kac’s original stochastic model and so had a purely classical context, free of formal analytic continuation. In the same year, Kauffman and Noyesproduced a fully discrete version related to bit-string physics, that has recently been developed into a general approach to discrete physics.