How to Distinguish Identical Particles. the General Case

TL;DR

This paper uses group theory to define and analyze the conditions under which identical quantum particles can be distinguished in complex systems, highlighting limitations and practical implications.

Contribution

It introduces a rigorous group-theoretic framework for distinguishing identical particles and clarifies the conditions and limitations for effective distinguishability in quantum systems.

Findings

Identical particles can be distinguished under certain restrictions.

Orthogonal projectors serve as effective distinguishing properties.

The framework applies to local quantum mechanics and nucleon systems.

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.