Construction of bosons and fermions out of quons

TL;DR

This paper develops methods to construct bosons and fermions from quon operators, which interpolate between these particle types, revealing new insights into particle statistics and operator relations.

Contribution

It provides explicit constructions of bosons and fermions from quon operators across the entire range of the parameter q, including paradoxical cases.

Findings

Bosons can be constructed from quons for -1 ≤ q ≤ 1, approaching q = -1 from above.

Fermions can be constructed from quons for -1 ≤ q ≤ 1, including q = 1.

The construction reveals paradoxical cases where particle types are interconverted.

Abstract

The quon algebra describes particles, ``quons,'' that are neither fermions nor bosons, using a label $q$ that parametrizes a smooth interpolation between bosons ($q = 1$) and fermions ($q = -1$). Understanding the relation of quons on the one side and bosons or fermions on the other can shed light on the different properties of these two kinds of operators and the statistics which they carry. In particular, local bilinear observables can be constructed from bosons and fermions, but not from quons. In this paper we construct bosons and fermions from quon operators. For bosons, our construction works for $-1 \leq q \leq 1$. The case $q=-1$ is paradoxical, since that case makes a boson out of fermions, which would seem to be impossible. None the less, when the limit $q \to -1$ is taken from above, the construction works. For fermions, the analogous construction works for $-1 \leq q \leq 1$, which includes the paradoxical case $q=1$.