Non-locality of Foldy-Wouthuysen and related transformations for the Dirac equation

Tomasz M. Rusin, Wlodek Zawadzki

Published 2011-08-20Version 1

Non-localities of Foldy-Wouthuysen and related transformations, which are used to separate positive and negative energy states in the Dirac equation, are investigated. Second moments of functional kernels generated by the transformations are calculated, the transformed functions and their variances are computed. It is shown that all the transformed quantities are smeared in the coordinate space by the amount comparable to the Compton wavelength $\lambda_c=\hbar/mc$.