Quantum stochastics: the passage from a relativistic to a non-relativistic path integral

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Abstract
Feynman's path integral for the one-dimensional Dirac particle uses paths for which Delta x approximately Delta t. For non-relativistic path integrals, typical paths satisfy ( Delta x)2 approximately Delta t (as in Brownian motion). The authors demonstrate the consistency of these two stochastic schemes and show how the relativistic formalism contains within itself the scale of the transition regime, namely Delta x approximately h(cross)/mc, the Compton wavelength.

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