Quantum Statistics of Identical Particles

TL;DR

This paper explores the broader landscape of quantum statistics for identical particles beyond Bose and Fermi, examining the theoretical consistency and implications of alternative statistics within quantum mechanics.

Contribution

It introduces a general framework for considering other possible many-particle statistics consistent with particle indistinguishability, challenging the conventional axiomatic approach.

Findings

Identifies alternative quantum statistics compatible with indistinguishability.

Discusses implications for the Pauli Exclusion Principle and superselection rules.

Analyzes state preparation and permutation invariance issues.

Abstract

The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical behaviors are excluded a priori. A more general approach is to ask what other many-particle statistics are consistent with the indistinguishability of identical particles. This strategy offers a way to discuss possible violations of the Pauli Exclusion Principle, and it leads to some interesting issues related to preparation of states and a superselection rule arising from invariance under the permutation group.