Localization and causality for a free particle

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 positive energy 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. (C) 2003 Elsevier Science B.V. All rights reserved.