Theories of violation of statistics

TL;DR

This paper explores various theories that propose violations of standard quantum statistics, focusing on quons which permit small deviations, analyzing their algebraic structure, implications, and potential origins of such violations.

Contribution

It provides a detailed analysis of quon algebra, superselection rules, and the implications of small violations of quantum statistics, expanding understanding of possible deviations from standard statistics.

Findings

Quon algebra allows small violations of statistics.

Superselection rules constrain observable consequences.

Potential origins of statistical violations are discussed.

Abstract

I discuss theories of violations of statistics, including intermediate statistics, parastatistics, parons, and quons. I emphasize quons, which allow small violations of statistics. I analyze the quon algebra and its representations, implications of the algebra including the observables allowed by the superselection rule separating inequivalent representations of the symmetric group, the conservation of statistics rules, and the rule for composite systems of quons. I conclude by raising the question of possible origins of violations of statistics and of the level at which violations should be expected if they exist.