Localization and Causality for a free particle

N. Barat, J. C. Kimball

Published 2001-11-09, updated 2003-02-28Version 2

Theorems (most notably by Hegerfeldt) prove that an initially localized particle whose time evolution is determined by a positive Hamiltonian will violate causality. We argue that this apparent paradox is resolved for a free particle described by either the Dirac equation or the Klein-Gordon equation because such a particle cannot be localized in the sense required by the theorems.