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 ≤ q ≤ 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 → −1 is taken from above, the construction works. For fermions, the analogous construction works for −1 ≤ q ≤ 1, which includes the paradoxical case q = 1.
The quon algebra describes particles, ``quons,'' that are neither fermions nor bosons. The parameter
q attached to a quon labels a smooth interpolation between bosons (
q=+1) and fermions ( $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$). Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. We generalize this and show that
qcomposite=qconstituentn2 for a system of
n identical quons. Using this generalization, we find bounds on possible violations of the Pauli exclusion principle for nucleons and quarks based on such bounds for nuclei.