Quon Statistics for Composite Systems and a Limit on the Violation of the Pauli Principle for Nucleons and Quarks

Abstract

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 ( $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}+1$) 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 ${q}_{\mathrm{composite}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}q}_{\mathrm{constituent}}^{{n}^{2}}$ 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.