Localizability and Elementary Particles

The well-definedness of particles of any kind depends on the limits, approximations, or other conditions that may or may not be involved, for example, whether there are interactions and whether ostensibly related energy is localizable. In particular, their theoretical status differs between its non-relativistic and relativistic versions: One can properly define interacting elementary particles in single-system non-relativistic quantum mechanics, at least in the case of non-zero mass systems; by contrast, one is severely challenged to define even these properly in the relativistic quantum field theories that now underlie the study of particle physics. Here, the impact of localizability on this status is reviewed in relation to the work of Paul Busch on positive operator valued measures that significantly probes the relevance of quantum unsharpness to it.