How to Distinguish Identical Particles. the General Case

Abstract

The many-identical-particle quantum correlations are revisited utilizing the machinery of basic group theory, especially that of the group of permutations. It is done with the purpose to obtain precise definitions of effective distinct particles, and of the limitations involved. Namely, certain restrictions allow one to distinguish identical particles in the general case of N of them, and of J clusters of effectively distinct particles, where N and J are arbitrary integers (but 1<J<(N+1)). Mutually orthogonal, single-particle distinguishing projectors (events or ptoperties), J of them, are the backbone of the construction. The general results are exemplified by local quantum mechanics, and by the case of nucleons. The former example suits laboratory experiments, and a critical view of it is presented.