On localized states for elementary systems

Abstract

We argue that the concept of localization for elementary systems is inherently ambiguous as in the example of an extended body in classical physics, and that there do not exist uniquely defined localized states. We discuss two sets of invariance requirements for the determination of localized states. Besides rederiving the results of Newton and Wigner, we study the consequences of postulated Lorentz invariance of localization. The corresponding Lorentz-invariant localized states are not uniquely determined. As all of these different types of states are completely equivalent, for all macroscopic kinematic purposes we have to accept all of them as possible candidates for localized states. We speculate that different types of elementary systems might require different types of localized states for their description. These localized states are useful for the enumeration of all possible relativistic wave functions, quantum field operators and relativistic wave equations one can associate with a given elementary system.